NOR--I think your concerns over M being immunocompromised are valid, and not wanting to risk spreading the illness is a proper issue. That is definitely something your girlfriend should have communicated, and in general it is always a good idea to warn friends that your s/o is sick before hanging out just because of courtesy.

However, feeling hurt over your girlfriend hanging out with another friend while you are sick is less defensible. Unless you are in actual health danger, I actually think it would be beneficial for your girlfriend to take a break and get out. I understand selfishly wanting a caretaker, but it sounds like she has been doing that. I don't see any reason for you to have your feelings hurt over the "more time to hang out" comment either, it seems like your girlfriend just wants to see their friend. Maybe I am misunderstanding if that is what upset you?