Well, it's no fun. I can promise you that. I am extremely needle phobic. When I was younger, I had crowding and my dentist wanted to pull teeth to help the others come in straight, and I was scared just like you are and I did NOT get them pulled. Now I have really crooked teeth and I always had decay between my teeth because they are too crowded and I can't brush and floss properly. So I have had a lifetime of toothaches, breaking teeth because they are weak, plus my teeth are ugly and it affects the way I feel about myself. Also, I will probably have to get all my teeth removed at some point and get dentures which is both a painful procedure, and painful everyday because dentures really don't ever fit right and stuff gets stuck under them etc.
As much as I hate shots, and I really really do...I can say it's nothing compared to the pain of not getting it done.
The good news for you is...baby teeth don't have roots so it won't be all that hard to get them out. Just a little bit of anesthetic is all it will take. You will be good as new the next day, and you will have room for those other teeth to come in nice and pretty.
Ask your dentist to give you laughing gas. It will really help you calm down. Also get your music so you can't hear anything, and keep your eyes closed. You will be done in a matter of minutes.