--yes, probably you do have nerve pain--along with a lot of good old regular nociceptive pain.

Sensations to vary from person to person, but nerve pain usually has a dysesthetic burning, cold, tingling, stinging, buzzing quality caused by actual damage to the nerves that are sending off inappropriate signals that the brain struggles to interpret, compared to the type of pain from other tissue damage that the nerves correctly interpret.

You may need a change in meds to get some/more relief--nerve pain is intractable in many people to standard pain meds such as Cox inhibitors or opioids; the first line for it tends to be anti-seizure drugs such as gabapentin or pregabalin and/or anti-depressants, in smaller doses than used for depression, such as amitryptiline.