Most areas have several family clinics/GPs where you can just walk in.
Do a google maps search for “clinic” in your area and check the reviews. Often you will see reviews in English from other foreigners, so you’ll have an idea of how well they deal with non-locals.
With these clinics, you just walk in, when the receptionist asks for your NHI card, tell them you don’t have and you want to 自費 (self-pay), and they will register you (there might be a form to fill in, which they can usually help you with if you can’t understand the chinese).
If you don’t have an ID card, take your passport.
The doctors generally can speak English if necessary.
The clinic will also give you the medicine after your consultation. Total cost will generally be much less than $1000.
If it’s a fungal infection which has got out of control, you will probably need to take a course of an anti-fungal pill such as fluconazole. if the creams aren’t working. This is something that a normal family doctor can deal with. (Actually you can get oral anti-fungals at some pharmacies without prescription, but it’s probably better you see the doctor in the first instance so you get the right dose and schedule.)
Going to a family clinic is a lot less hassle than going to a hospital, as with the latter you will have to first register with their front desk, then make an appointment booking with the specialist, and end up spending half a day hanging around the waiting area with loads of other sick people to see when your number comes up.