How can I tell if my elbow is broken or sprained?

Elbow sprain. Typically sprains heal over 6-8 weeks, however severe sprains or complete tears sometimes require reconstructive surgery. Initial rest and ice with anti inflammatories help. If your elbow moves but is very painful, or if you cannot move it at all, i would see your orthopedist to rule out a fracture. Fractures may having a catching or crunching feeling when trying to move your elbow.
Get examined.. It is impossible to tell what you have based on the information/question. The mechanisim of injury(how you got hurt), the amount of pain, degree/range of motion you are able/not able to do, visible deformity etc..Are important determinants of the severity of your elbow problem. Xray/mri may be needed to evaluate fracture/ligamentous injury etc..If u r having much problem, consult doc. Good luck.