First of all, you're only 16. You cannot legally get a tattoo until you are 18. Yes, there are tattooists who WILL tattoo you. But a good, reputable one won't. And trust me, if you want a decent tattoo, you need a decent tattooist! So there's you first problem!
Secondly, yes, tattoos hurt. Anyone who tells you differently is a liar. People have different levels of pain tolerance so it's difficult to say exactly how bad the pain is, but it's not mild. The first part of your session will hurt a fair amount. After a while it does start to get kind of numb and it doesn't hurt quite as much. It's not comparable with what you described, at all. I don't know how to describe it to you .. it's like a deep and very sore scratch, but one that doesn't end quickly as a scratch would. The pain is consistent until it starts to numb a little.
Having said that, thousands of people have tattoos! It's not an unbearable pain and it's not going to kill you, lol. But despite what you said, I strongly advise you to wait until you are 18. Not because I think you'll change your mind, but because you should use a tattooist who takes his business seriously and is not prepared to break the law.
have many tattoos myself