Hello,
It can be due to eczema skin which presents as red, dry itchy flaky rash in response to an allergic reaction. You can apply some calamine lotion at the rash as it will help in soothing the skin. You can take some OTC oral antihistamine medications like Benadryl or Claritin and see if it helps.
For mild-moderate symptoms a weak steroid may be used (e.g. hydrocortisone as dermacort), whilst more severe cases require a higher-potency steroid (e.g. clobetasol propionate, fluocinonide).But they are available under prescription and should be taken only after consulting a dermatologist. Symptoms can be exacerbated by dryness of the skin. Use good quality moisturizers to prevent moisture loss from the skin.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.
I forgot to mention it could be a little patch of a fungal infection of some sort. Lotrimin cream might help in that case, but you might want to see a dermatologist.
It could be due to food allergy such as dairy or wheat/gluten.
It could be contact dermatitis, so pay attention as to whether you rest your chin on your hand or arm or anything else. It might be an allergy to a particular toothpaste.