PA-28 pilot reported flat tire on landing that cause the aircraft to veer off centerline.

Narrative

Upon touchdown on Runway XX centerline at ZZZ Aircraft veered right 45 degrees. I applied full power to start go around. Upon returning to ZZZ Runway XX I assumed a right main flat tire or brake locked up as I smelled burnt rubber after starting full power go around. On approach landed left side of runway with full flaps to minimize touchdown airspeed. Upon touching down aircraft veered to the right again and was able to stop short of edge of right side of runway. Right mail was flat a Runway XX -XY was closed until Aircraft could be removed from runway. Upon inspection of airframe left trailing underside of wing had impact marks starting about 12 inches and flap that had been in the 2nd notch extension received damage from what was a runway edge light. Tire was removed showing no skid flat spots but did have a small cut that could not be determined by visible inspection had come all the way through tire and tube. Cause of flat could not be determined if tube failure or FOD on runway.