Urgent care centers can sometimes give pain medicines and prescribe pain medicines but not all urgent care centers can give or prescribe pain medicines.
Sometimes you'll be referred to your doctor to get pain medicine prescribed or be told to go to the emergency room if you really need some pain medicine prescribed to you.
However all urgent care centers stock medicines and antibiotics that they can administer and prescribe and sometimes you can get your prescription filled right at the urgent care center depending on the urgent care center.
When I went to urgent care I was referred to my doctor to get prescription for a prescription pain medicine but they were able to give me some of their pain medicine.