Can my ribs pop out because of doing chiropractic exercises?

Hello doctor,

I am 50 years old with a height of 5 feet 2 inches and a weight of 110 pounds. I recently started chiropractic treatment for my back and neck pain. My chiropractor also taught me exercises that I should do at home daily. After about two months of two chiropractic sessions per week and daily exercises, my neck and back did get better. However, I realized that one of my ribs about two inches below my collarbone was popping out. I had trouble breathing for about two days since my rib popped out. After about two days, the breathing problem subsided and there was no pain in the area. It did not hurt when I pushed down on it. I consulted my chiropractor about this problem and he said that my ribs were misaligned due to one of my daily exercises that I was told to do. That particular exercise involved pulling on a band with my shoulders. I feel like my ribs were misaligned due to the chiropractic sessions when he was pushing with pressure on my back and not the daily exercises. My chiropractor said that this could happen and there was nothing for me to worry about. He also said that I should continue doing my daily exercises. I do not know if I should continue to trust him or consult another doctor. Can my ribs really pop out because of shoulder exercises with a band?