You know dandelion, right? Just buy those dandelion roots. You'd better take some dirt with you and don't need to clean it. Then buy alum, and then crush the roots of dandelion with alum in a garlic mortar, not like foam, just a few times. The amount of alum depends on your paronychia!
Maybe not in a week, but in half a month!
I had paronychia before, and I'm still studying, but my grandmother is a great doctor. Hee hee.
I wish everyone a happy and healthy life.