Did the doctor describe it as "contact dermatitis?" Irritation around the mouth is often due to cold sores, a virus; ringworm, a fungus; or psoriasis, usually due to an auto-immune disorder.
I get frequent bouts of psoriasis due to an auto-immune disorder (Hashimoto's thyroid disease). Scalp, hands, sometimes around the jaw and nose. Nothing to do with anything I've been in contact with. I don't seem to be allergic to most ordinary products and foods, soaps, etc. No doctor or endocrinologist has been able to determine what provokes the occasional symptoms. I've cut back on ibuprofen and NSAIDs, which seems to help a bit. But it's still a mystery.
Regarding "natural" vs prescription remedies, I'm a skeptic. Very rarely have I found any alternative remedies to be more than a placebo, and some are actually harmful. Generally speaking it's better to go with what a dermatologist or other specialist recommends, whether prescription or OTC.
I haven't found any "natural" remedies that work as effectively as well researched OTC and prescription topical ointments and meds for skin problems. The closest you'll find to a "natural" remedy that's also recognized for being effective on psoriasis is salicylate cream -- Aspercreme or anything comparable, even from the dollar store. Salicylates were derived from natural sources -- willow bark is the common reference. But it makes better sense to take an aspirin or use an ointment containing salicylates than to brew up our own stuff from tree bark.