Hello!
Avoid forced extension in the acutely swollen finger, rather, position the finger in hyperextension after the swelling has decreased.
I would suggest you to take NSAIDs and apply ice packs and also get yourself examined by an orthopedician and go for an X-ray for proper diagnosis.
Take care!
Ouch, sounds pretty painful. Hopefully there isn't any tendon damage or anything like that. If I were you I'd head to the doc and get it checked out. Splinting it is good to immobilize the digit. While it isn't going to fix the problem, it will limit possible further damage by accidentally hit it on something. I would definately do that and do not take it off until you are advised by the doctor. Ice it down to help with the swelling and possibly take a pain reliever.
Any discoloration to the finger? How about to the rest of the hand? If it's broken, there really isn't much that can be done. But given how you described how the injury occurred, you may have torn something. Just my opinion, I'm not a doctor. Hope it helps a little and that your finger feels better soon.