I was arm wrestling and since then my wrist sounds when I spin it and it feels like two bones are rubbing each other, but it doesn't hurt.?

Not to worry. There are numerous causes of wrist popping. We rarely are concerned if there is no pain associated with the popping. If you are concerned, then a visit with an orthopedic specialist can shed some light on more specific causes and whether any precautions or treatments are necessary.
Injury. Like most injuries a strained wrist is caused by excessive force or repetitions. The sounds should subside if you give it time without further aggravation.