I might have dislocated an elbow. Is it a good idea to place elastic bandage to compress it?

Get an xray. Christy, it is very difficult to sustain a dislocaion of an elbow in that it takes a signicant impact for that to occur. Rest and ice and support for now. Avoid an ace wrap as this may cause swelling above or below the elbow. It is very important for you to get an xray of your elbow to get a correct diagnosis. If the xray is abnormal, you need to followup with an orthopaedic surgeon.
No. An elbow dislocation is a severe devastating injury that would send anyone to the emergency room immediately. An x-ray is needed to make a diagnosis.