My 5 yo DD recently had a red patch like that. I thought it was from daddy's unshaven face. But it lingered then turned dry. I do think it must be allergy related but k=can't figure out to what. She is allergic to dairy, egg, peanut, tree nut and shellfish already.
I was starting to think just teething, but mow I don't know.
How long has it been there? If it's something like eczema you could try rubbing some coconut or olive oil on it a few times a day and see if that helps. Does it look like a bug bite? Have you changed laundry detergents, etc.? I'm sorry I'm not more help!