I have a welt like rash that is spreading slowly towards my armpit, and also on my upper inner thigh. it is non itchy. is it cellulitis?

Could be: It could be hives. Please see your dermatologist for evaluation and to discuss treatment options.

Many reasons: There are many causes of what you describe. A contact allergic reaction (though that would probably itch), a fungal infection, infected hair follicles as doctor said, a dermatologic rash, ongoing trauma from you scratching it, etc. After taking a good history and doing a good exam, starting treatments may include anti-itch or steroid meds either topically or oral. Antibiotics are not needed.

Doesn't sound so: Many things can cause this. To start with use a fungal steroid cream over the counter twice a day on the areas and see your doctor.