It is absolutely NORMAL to need prescription pain meds for several weeks (or sometimes even months) following surgery. If you have pain, you need medication. So don't hesitate to contact your doctor now. Don't wait for the meds to run out.
Because they are controlled medications, doctors always write the prescriptions for no refills. That doesn't mean you can't have refills. It just means you have to communicate with your doctors that you need another prescription so they can monitor your progress in recovery. Your GP can write a prescription for them as well. It doesn't have to be the surgeon.