I think you have first figure out if he has ADHD or not. He either has it, and the doctor didn't diagnose it last year (maybe because the doctor had limited exposure to him, unlike the preschool teacher; or maybe because you were upset and didn't want that diagnosis you presented the facts in a little bit of a slanted way); or else he doesn't have ADHD, and there's something in the way ou are talking to him that he isn't taking seriously.
Little kids (particularly boys a good part of the time) are really active, and if their mother didn't start when they were really young, telling them things like, "Don't run around while I'm in the bank. You can run around later, but the bank people don't want children running around," children just kind of get used to running around everywhere they go. Then the parent starts kind of uselessly calling the child's name, and the child ignores the parent, and the parent does one thing or another (its sometimes different each time), but before you know it the child is running around "crazy" again, the mother is kind of half-heartedly and fruitlessly calling the child's name, and on and on. The child has learned that he doesn't have to take his ever-talking or scolding mother too seriously. Is there any chance this is how it is for you? Are you super-syrupy-nice to him all the time because he's little? (They don't see that as authoritative enough.) Are you instead always just kind of yelling and nagging but allowing him to ignore your words? (They tune that out after a while.) Do you generally act like a leader and present the rules (nicely but not syrupy-sweet and baby-tone) as if there is simply no option but to go with them? (That's what children respond to.)
When children (who don't have ADHD) have a mother who just kind of firmly explains to him, "We're going to the Post Office. While we're in there you need to stay right next to me, and when we get to the mall I'lll buy you a little treat," they usually just accept the rules that have presented as if there is no option but to follow them.
If you tell a child there are places he can run (out in the yard, at the park, maybe in the family room, etc.) and places he needs to sit or stand next to you until you complete your business somewhere, it makes his brain start to process the idea that he must control his own behavior.
Children do well with some basic rules. When my kids were little I pretty much let them do whatever they wanted as far as playing or leaving the table went. I had the few, basic, rules, though, that they were just expected to follow: No running around crazy in the house except for in the family room, no throwing balls in the house, no hitting anyone. They knew that they could run around as crazy as they wanted outside or run around "slightly crazy " in the family room. They also knew if I were bringing them to a "business place" the visit wouldn't be long, but while they were there they were to stand right near me and not be running around or being loud. They knew if we visited someone who had children they could play but follow the rules of that house. When we were in stores they needed to stay with me. (I'd explain, "I don't want to lose you" and "The store people don't want their things knocked over.")
My point is if a child knows he isn't being told he can't run around like a wild man and that he's just being told he needs to be a wild man in the right setting he has both freedom and structure; and structure is something children who are very active need - just some guidelines that are all "written in granite" so the child doesn't have to figure out what the rules are or aren't by himself.
When children do have ADHD one thing teachers do is provide a certain amount of structure. Too much structure isn't good, but just those basic and unbendable and fair rules help children get used to the idea of self-control but also helps them to be children people don't hate to see coming. As a result, it helps their self-esteem because people respond well to them and welcome them more than they do with a child who doesn't behave.
If you just tell him, too, that he has to hold your hand when you do something like walk through the mall or cross the parking lot, or if you ask him to choose between standing on the front of the shopping cart (while you hold it at all times) or sitting in it he gets to choose but one of the options isn't running through the store.
When you go out with him, do you enjoy being with him and treat every trip out as a pleasant thing? It sounds strange, but a child that little can enjoy a morning afternoon out with his mother, doing errands, if it feels to him as if its special time together. Just because you're going to the bank it doesn't mean you can't make it nice time together. The other part of telling a child something like that he can't run around the bank is to talk in simple terms about what the bank is or why you're going there. ("We're going to go get lunch, but first I have to go to the bank for just a minute so I can get money." or "Hey - would you hold onto this card we need to mail for Freddie's birthday? We need to go to the Post Office. Do you think you can remember to tell me I need to get stamps too?")
If you treat every place you bring him as a little field trip, and treat your time together as if the two of you are not only a team but a great team together it can make children feel more special and be more inclined to want to behave because they enjoy being treated as your little buddy.
If you behave as if you're the leader of the team, he will look up to you and want to follow the plan (provided, of course, he doesn't actually have ADHD). If you take the approach that "I'm not always after you or on your back but for the little while we are in the car insurance office you do need to sit quietly" he may start to see that as fair, but also it won't be as if he's being expected to be a little, oppressed, silent, boy all the time but instead his usual self (except for those brief visits to certain places).
Usually, this type of approach works well. Don't expect him not to act like a Buckingham Palace guard but also don't give him the chance to start running around or climbing over desks. Hold his hand (not like you're confining him - like you like him so much you enjoy holding hands with him).
When it comes to sugar, I always doubted it when people said sugar made their children hyperactive because I know, myself, that there have been times I've been a little hungry and not been able to sleep, so I'd take a cookie and find I could then sleep. Several months ago the program 20/20 had a show on about myths; and John Stossel talked to doctors or scientists or whoever, and it was said that sugar doesn't make people hyperactive. The thing on the show was how even with experts explaining that the was a myth all kinds of people still believed sugar made them nutty. They noted that some people think kids at birthday parties are nutty because of all the sugar, but it was said that it is because a bunch of kids are together that they get so loud and sometimes crazy acting.
Also, although it isn't good for anyone (particularly adults) to have too much fat, children need a certain amount of it for their brains. My son, who used to be a little tense in school, would come home and have a big glass of whole milk and feel calmer when he was ten/eleven or so. He was a slender kid, so it didn't pack pounds on him. So, if you're thinking about adjusting your son's diet you may want to check with the doctor about his/her opinion of whether whole milk is what your son should have.
Another thought: Make sure time of day (as well as place) has a few basic rules. Active play is for all day, but after dinner tell him that its time to do something like play L'egos, look at books, or just play something that isn't running around and jumping. That helps an active child start to calm down before bed. You know, yourself, that exercise makes people feel invigorated. (By the way, a lot of seemingly hyperactive children will suddenly sit for long periods of time when they have a big pile of L'egos to play with. Maybe that's one way to figure out whether he's really got ADHD or not - how long will he sit and play L'egos.)
If he has things like building sets or play sets or even things like playing trucks or PlayMobile people after dinner, from there you could give him his bath (also calming) and let him watch television or a non-action video until bed (at 8:30 or so - 9:00 for now if he absolutely must).
After dinner, too, if you kind of make sure your house doesn't have all kinds of loud talking and bright lights and loud televisions etc. it can help. You don't have to have it be like a museum, but keeping things a little quieter than you may have them at 3 in the afternoon can help make a child wind down better.
Well, I don't know if any of the thoughts I've offered are things you already do or not, or whether anything I've said is at all useful or informative, but I know how much mothers want their children to enjoy school and thrive in school. I just thought I'd offer you as much as I have just in case even a small part of it will help in some small way. (I have a "thing" about children and school.)