"Bust my chops" is an idiom, in which the word "bust" means "hit" and the word "chops" means mouth. These are slang terms, combined within a single idiom. So, if I said, "he was busting my chops", the literal meaning would be that he was hitting me in the mouth. However, as an idiom, we know that we are not to interpret it literally. Another way of saying "he busted my chops" would be to say "he gave me a hard time", but of course, that's another idiom! In both cases, the meaning is that someone is deliberately making a situation difficult for someone else. Someone may "bust my chops" in a teasing way, or in a mean way, but in either case they are making a situation difficult for me.

Expend much personal effort; exhaust oneself. "I busted my chops all morning and this is all I get?"