My boyfriend gets annoyed when I am around him sometimes.
That sounds odd, any reason why?
He gets frustrated over being sick all the time. It makes him irritated to have me around.
It is unfortunate that him getting sick makes your presence annoy him. Try to find ways to help him out without being near him, or try and prevent him from getting sick.
Nah fuck that, I'm not dealing with this.
The way you are talking makes me think this relationship won't work out. You need someone who respects you and he needs to get better or take some time off.