It means you are really irritating me now, so much that I can't concentrate properly.

As I understand it, "to do something in" is a slang expression meaning "to cause great problems for", "to ruin" ... something like that. So, to do someone's head in, means to cause them great mental distress. Here, "head" means "mind" or "brain".

It seems like one character is saying "the things you are saying hurt my head. Stop!"

It means "you are annoying me".