Since you have quite clearly identified your pelvic pain to be worse after your period and with orgasm, you may benefit from removing the IUD. The potential advantages should be weighed against the loss of contraception and the return to normal menstrual bleeding.
Unfortunately, there is no guarantee that your pain will be alleviated by removing the IUD. There are other sources for chronic pelvic pain, including the pelvic muscles, the bladder, the lower intestinal tract, and the uterus.
Make sure that you discuss your concerns with your gynecologist. An updated pelvic examination and pelvic ultrasound may be helpful in the decision making.