I slammed my finger on a table i bruised and got swollen instantly then hurt real bad then started throbbing and now its both..is my finger broken?

Need an xray: It is difficult to say whether you have a broken finger without getting an xray. Your finger could have ligament damage or have a bone contusion as well. However, a fracture is a distinct possibility. I recommend an evaluation by a health care professional who should get an x-ray.

Hematoma?: Sounds like a contusion or hematoma you should try ice and nsaids if it doesn't start to improve consider an xray.