I'd probably just go to a centro de salud.
One year I had very bad bed bug bites and went to the pharmacy to buy a cream. The pharmacist told me, if it doesn't get better, I need to go to the urgencias. The over the counter cream didn't help at all, but I was lucky and another pilgrim had a cortisone cream which he gave to me, so I could avoid the urgencias that year.
But when I got a very bad case of bed bug bites again in another year, I remembered the pharmacists advice and just went directly to the Fromista centro de salud during their "urgencias" hours and they gave me prescriptions for several different medications including cortisone and antibiotics. So I guess that might work for your problem.
Not sure if this is the "correct" way to do it, but it is what I learned to do from the pharmacist (and also the hospitaleros, who send me to centro de salud when I had a bad chest infection with a fever and needed antibiotics) and it worked.
I only had to show my European health insurance card and passport, didn't have to pay anything apart from a few Euros for the medication in the pharmacy.
By now, I've been to the centro de salud in Carrion, Fromista, Piedrafita and Triacastela. One even had a translation sheet for pilgrims, and three out of the four times there were other pilgrims in the waiting room with me. The staff was always friendly and seemed to be used to see pilgrims.
Get well soon!