Unexplained rash on face for 3 months

Hi. I am so fustrated. I am hoping someone provide some words of wisdom. My 11yr old son has had this rash on his chin and jaw line for about 3 months now. It doesn't itch or bother him at all. Its just red and bummy. We have been to see the dermatologist a few times. He originally diagnosed it as perioral dermatitis and gave us a script of Clindamycin to use topically for a month. That did nothing so then he changed the diagnosis to lichen nitadus (sp) and gave us a script for Locoid. The Locoid made his skin mad so the derm changed the topical to Elidel. That seemed to reduce the redness and inflamation but the size of the rash is still the same. Now he added an oral antibotic, Cephalexin (since he is allergic to penicillian) that hes been taking for 5 days along with the Elidel still and said maybe it is perioral dermatitis. No improvement still. Any ideas on what this could be...or how to treat it.