Will I need a pelvic exam?

You'll get both a pap and a pelvic exam. The pap hurt (I'm 19 now, but I was 18 when I went. Maybe me being a virgin, and me being very tight naturally was he issue. Even when boys would finger me, it would always kind of hurt.) the pelvic exam for some reason, either didn't hurt st all, or hurt a lot less compared to the pap.

I also went to get birth control for bad cramps

Whether they'll need you to have a pelvic examination depends on their practice, given your age and that you clearly have a health problem it would be recommended anyway even if not for birth control. A pelvic examination shouldn't hurt at all as long as you're relaxed and they are gentle, but of course it does depend on what's causing your menstrual cramps as this may result in some tenderness during the examination. If it hurts tell them.

Birth control is for birth control, stopping your menstrual cycle isn't a healthy way to deal with cramps - why not ask the gynecologist to investigate and treat cramps instead of risking your health trying to temporarily hide them?

You will and it does not