I hurt my wrist and now my little finger pops when i close my wrist, should i go see a doctor and if so what type of doctor?

Trigger finger?: This sounds like a trigger finger. Sometimes in more severe cases the finger gets 'stuck' and straightening it out is painful. If it is just clicking, it might resolve by itself. A cortisone injection can be very helpful (orthopedics or rheumatology), but you can probably wait and see.

Wrist injury: Sounds like you may have hurt more than just your wrist. Regardless, i would see a hand doctor who should be able to help you with a good history, exam and likely x-ray. Good luck.