Is it okay to play badminton as I get older?

I started playing badminton when I was 52 years old, and now I am 60. Since I started late, I made a lot of efforts to avoid injuries. I always do thorough warm-up exercises and muscle training. Fortunately, I have played well without injuries so far. However, lately, my arm muscles haven't healed and still hurt. After playing, my shoulders and elbows always hurt. When I don't play, it's okay, but after playing, the pain is intense. I try to play carefully, but can I continue playing badminton in this condition? I heard on television that overuse injuries can cause muscles to be permanently damaged and unable to recover, which makes me very worried. I want to play badminton for a long time, but is it okay?