Typically, your hormones never leave normal when one testicle is removed due to testicular cancer. However, your boyfriends behavior is NOT typical. About 17% of the time the man with need some sort of hormone supplements because the remaining testicle cannot pull its weight. His behavior is quite classic for someone without enough testosterone - erratic, loss of libido, mood swings. I suspect that he is also fatigued and depressed.
Seriously - he really needs to be tested. They need to test, at a minimum, his testosterone, LH and FSH. There are various ways to supplement, including shots, gels, creams, patches and a few others. I suggest that he first get a shot and see how that works - that it actually brings him back to normal. It would be good to see an endocrinologist, but very few actually know anything about testosterone. You could call around, or maybe just send him back to his urologist.