I fell from my bike and hurt my right hand. Will I be able to play the guitar again?

Fretting after fract. Sorry the pun but there is an old surgical joke: "could you play the guitar before?" in all likelihood with a properly managed injury satisfactory healing and with follow up care, you should be able to play with minimal impairment.
Probably. Without out knowing your specific injury, one cannot give an absolute answer. However, most injuries treated properly usually will allow one to recover and function normally. That is, almost everyone will be able to do everything they could do before they were injured.