No they don't give you a pap and my sis was on her period and they just glaced down there. Our MEPS experiance was super easy...we both got a picket fence and we are both older her 24 and me 37 :) it will be fine I promise.
I didn't get one, however they DID make me strip butt naked and wear a paper gown. I was told to sit on a table with stirrups and had my breasts examined, and I had to spread my legs but the doctors only took a quick look, then I proceeded to do the funny exercises and duck walk.
The only thing I wasn't expecting was that I was told by my recruiters that the "underwear olympics" was done in underwear, however I did mine naked in my paper gown. Then again I was the only female there that day, so they might have skipped a few processes to save time. I don't know.
No you will not get a pap smear at MEPS. They will just take a peek down there and that is all. You will do a serious of movements in your underwear with other females in the room. It will be a long day of sitting around.
Military doctors aren't that bad get used to it because you will need to get an annual pap while in the service. In some cases though if you have normal paps you might not to go every year.
They used to do pelvic exams with a speculum, etc., or if you were chaste, they would do an anal exam instead. (They don't do either these days.)
I used to tease the gals I recruited back in the day that if they were receiving a pelvic exam, and the doc's hands were on your knees, there was a problem...
No pap smear.
No pelvic exam
The doc will simply take a quick look to make sure you've got what you're supposed to have and that it's all where it's supposed to be.
"I've heard the people are rude and rough"
This is just a hunch, but if you're "nervous as hell" about how you'll be treated at MEPS, maybe the military isn't a good choice for you.