Pilot reported they encountered a wind gust on short final resulting in a hard landing and a tail strike. They did not realize they had a tail strike and on a subsequent approach landed hard on the left wheel causing the tire to come off the wheel hub.

Narrative

Due to the wind conditions; I should not have flown. I gave into what I felt was a pressure that I needed to fly; and that was my first mistake. I flew one lap around the pattern; landed; and my landing was smooth. I went around one more time; and upon landing; I encountered a gust of wind. When that gust went away; the plane fell onto the runway rather than landing smoothly. I didn't realize it at the time; but the tail of the plane hit the runway and the tie down ring was snapped off along with some other damage. After that landing; I realized that I should have come in with less flaps and a higher airspeed. On my last landing of the day; the tire came off of the rim. Originally it was thought that the tie down ring popped the tire and caused it to deflate. The plane had to be tugged off of the runway. Later it was found that the tire actually came off due to a side load; and was not popped. As far as I could tell; my last landing was the smoothest of the day; and I don't remember being sideways at all; but some side load was imposed on the tire causing it to come off of the rim. Airport authority then found the tie down on the runway after I informed the tower about my situation.