For a week I've had a quite itchy and dry traveling rash on my face/neck. It started at the corners/inside my mouth after eating old cheese. Cure?

Penicillin mold ? Penicillin mold has been known to grow on cheese. See a physician to make sure that the rash is not a penicillin allergy rash. Take some of the old cheese with you.
Rash on face. I cannot be at all certain what this is, but it is reasonable to say that the first thing you could safely try would be over-the-counter 1% cortisone, twice a day; give it 4 to 5 days; if not better, see an md.