No it's not, yes they hurt and no one will see it, you will hurt your lip if you want to see it or show it to other people, you will hardly see it, and there will be no point. Why not on your arm or something?
Yes, of course it would hurt. I would recommend that you don't get a tattoo since when you get older it will just start to look bad. Also the fact that you had to ask random people shows that you probably shouldn't get a tattoo if you have to question it.