The solo student pilot reported that, during the landing roll of a touch and go landing, the airplane began to veer off the runway, so he added power for a go around. He called the tower controller to inform them of the go around and he observed the left landing gear strut was bent and the tire was "missing." He told the controller that he must have hit something and was instructed to fly by the tower. After the flyby, the tower controller confirmed damage to the left landing gear and cleared him to land. The student landed and, during the landing roll, the airplane skidded off the runway. The airplane sustained substantial damage to the left horizontal stabilizer and left elevator. The student pilot reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation. The automated weather observation station located on the airport reported that, about 7 minutes before the accident, the wind was from 320° at 8 knots. The student pilot was landing the airplane on runway 21. Examination of security videos revealed that, during the first landing and go around, the airplane drifted to the left and the left main landing gear struck a runway sign.