Broken arm, swollen fingers?

Yup, you should expect lots of swelling. The only risk there is that the swelling develops to the point that it restricts blood circulation. Keep an eye on your fingers, if they get tingly or if they're cold then you need to get them checked - one way to check the circulation is to pinch or push in the tip of the finger, it should go white, then when you release it the colour should come back within 3 - 4 seconds. Longer than that get it checked by a doctor. If you think the circulation is being restrcited then it's really important to get it checked quickly as possible as restricted circulation can cause long term damage.