What sort of medical person would be ok with anecdotal advise based on extremely limited information and no knowledge of the case vs going to see a doctor? And would suggest any topical lotion prior to assessment and diagnosis? You said "get a tube of hydrocortisone. That should clear it up quickly" No reference to personal experience, medical training, or the like. To my thinking, that's medical advice of the sort that is best not indulged in on forums (or at least not heeded).
My tube of cortisone says "temporary relief of minor skin irritations" and while I have lost the insert, it contains warnings that include a time limit for applications (3 times daily max, for max 7 days). While it does list specific skin conditions, one would need to know it was in fact eczema, a reaction to jewellry, etc in order to adequately ascertain proper useage.
Sorry, I don't find your rationale compelling, and as someone else mentioned, facial 'rashes' can signify other issues. Now...getting the OP's mom to actually GO to a doctor sounds like it might be a bigger initial hurdle
I don't want to argue the point further, since the OP has chimed in that a visit to the dr is on the books, and that's what matters most, but having worked in a pharmacy for some years, I know I wouldn't be comfortable advising a treatment based on what we know in this situation (vs, for instance, something specific like "I fell into poison ivy, what would you suggest")....nevermind that unless you are a licenced pharmacist, it is actually illegal to recommend medication as a pharmacy tech here. Perhaps it's different where you live, but I've been trained to avoid doing so.