A few months ago I got my basal cell carcinoma removed and it has been stinging. Is this something to be concerned about?

See your doctor. It's always a smart idea to play it safe when you have questions about surgical recovery. In the vast majority of cases, your symptoms are likely related to healing and residual inflammation. But if this sensation is not getting better (particularly after a week or two), it is wise to go see the doctor who did your surgery and get examined.