is my finger broken or not?!

You may have some tendinitis in that finger. Depending on how bad it is, here is what you can try:

Ice for five to fifteen minutes at a time on the area which is most swollen and tender.
"Over the counter" non-steroidal anti inflammatory medication (NSAID), such as aspirin, ibuprofen, naprosyn, or ketoprofen. Check with your pharmacist regarding possible side effects and drug interactions.
Avoid activities which involve a sustained grip. Hold off on the use of grip strengthening devices or exercises involving repetitive squeezing - these put stress on the irritated tendon.
If fingers bend and lock during the night and are painful to straighten in the morning, it may be helpful to wear a splint to keep them straight while sleeping. One way to do this is to use a wrist support splint as shown below: A wrist splint designed to be worn on the opposite hand may be worn with the forearm end turned out to form a palm sided support for the fingers. This may be helpful as an interim measure.

http://www.eatonhand.com/hw/hw022.htm