ADVICE PLEASE: Complicated Contraception Question

I have been taking birth control for 7 years because I would get extremely sick from my periods. When I started taking it I was a virgin (not the case anymore); I am still a dependent on my parents insurance and am still a student and have no money. My birth control was extremely good to me, it took away my periods (doctor was aware and ok with it) for 8-months at a time. Recently I went on a new medication that interferes with the contraceptive part of the birth control. I do not want to stop taking my actually birth control. Ecaudent keeps my sickness at bay. While this was not a concern to me initially, it is now. I cannot tell my parents it is a concern, but my partner and I are struggling with condoms and I do not know what the best form of contraception is for my situation I feel like the IUD would be great but I cannot get that without my parents knowing because it would be on insurance. I feel that the female condom would give my partner the same issues we were having with condoms. I feel that the cup/sponge would be uncomfortable for my partner as he would be able to feel it inside of me (is that the case?). I read on the Planned Parenthood website that pulling out is a fairly good method with only 4/100 women getting pregnant, which is less than the other methods when done properly, but I am truly at a loss here... please help me out eve-goers!!!