I don’t have specific advice for León, but at least in a city and midweek, there are lots of options.
When I have needed medical help along the Camino, which has been several times, I asked at my lodging (best) or looked online (not the best, but when you’re desperate, it will do). I wasn’t concerned about price because 1.) I needed the help, no matter the cost; and 2.) medical care in Spain is inexpensive. I paid about €50 each time to get treatment from a pt, and maybe €75 to get urgent care at a private hospital. X-rays were another €75, as I recall. I never had X-rays at a pt, so not sure what they would cost, but probably about the same as at the hospital would be my guess. I was not charged for ultrasound imaging by any pts, which may be all you need for a soft tissue injury.
Public clinics may not see you because they are just for Spanish people. Non-urgent care at a private hospital will require an appointment perhaps days or weeks in the future, and a much higher fee. So if you do go to a hospital, be clear it’s for urgent care.
I hope that helps and you are pain free and back in action soon.