No, I don't think it's fungus, so I wouldn't use athlete's foot cream. I think it's more likely to be eczema, so I'd start with over-the-counter hydrocortisone and vigorous moisturizing with any lotion you like. If that doesn't clear it up, a visit to a dermatologist should give you the diagnosis and treatment you need promptly.
I'm confident that you're not contagious.
Best.
Dr. Rockoff