I have the exact opposite of your problem, but I get the same result. I rarely have periods and every doctor I've talked to just wants to give me birth control, but I refuse to take it. Honestly, I've given up trying to fix my issue because fixing it is more trouble than the problem itself, but I hope you don't give up.
Personally, I wouldn't go as far as a hysterectomy; you should suggest an IUD to the next doctor you talk to and hopefully they'll actually discuss the idea with you. The Mirena IUD is supposed to be really helpful with heavy, painful periods. Good luck.
A hysterectomy is really really really difficult to obtain at a young age. I have a friend who has been seeking one since 18 because of a genetic disease she has, she refuses to get pregnant. She's 23 now and her doctors are still saying, no you're gonna change your mind. Even my mother in law had difficulty obtaining one in her 30's for bad pms symptoms and cramps. I'm not saying it's impossible but that's what you're up against. Also the hysterectomy will only stop the period and cramping from the period. Besides possible hormonal influences I don't know if it would have any effect on your ovaries or prevent ovarian cysts. And I know it won't prevent ovarian cancer. If you're serious about a hysterectomy, I think the best way for you to get it is to possibly keep switching doctors. I have found that female doctors are typically more receptive to such problems. I also have found doctors sometimes need you to be assertive to really know how much you want the procedure. If you know what you want, don't stop until you get it.
As far as sex goes, have you mentioned that to your doctor? No amount of BC I know of will fix that symptom and she really needs to pay attention to it. Have you had any abnormal pap smears? Sometimes that can cause painful sex. However, it is also possible to be allergic to a guy's sperm, lubricants (even water based), and the spermicide in some condoms. I would suggest to experiment a little to see if it's the lubricants you possibly use, the condoms, the guy, or the action, or a bizarre mix of any of them.