I don't mean to be rude, but if you want a full answer of what is wrong, then I would ask for a referral and I would encourage you to take all the tests offered. Yes, they may be invasive or uncomfortable, but they are done for a reason - to gain information. By thoroughly gathering the best information means that they have the best chance of helping you. An internal scan is very quick and by no means painful.
That said - there is little point you going through any of the tests if you are simply dismissing the likely treatments at this stage. Average age to start your period is 12, you say you have had them for 8 years, making you a roughly 20 year old woman. It's none of your family's business what treatment you require to deal with this pain that sounds so debilitating. If the treatment they give you for this specific problem has the side effect of also being a contraception - so what? It doesn't mean your moral compass with go out of the window and you'll be jumping into bed with every man you meet (in fact a lowered sex drive, ironically, is a common side effect of many types of hormonal birth control).
This is nothing to do with your family - this is about your health and what is best. Keep your family out if they will interfere and take a trusted friend. My strongest advice would be to battle through the tests (even if briefly invasive/uncomfortable), get the results you need, take the drugs you need and get back to a normal life. A five minute examination has to be way less of an issue in the grand scheme of things.
Good luck