Is it possible for your elbow to pop out of place if its already been dislocated before?

Yes: Once the dislocation has been reduced back into place and held in a splint for 2-4 weeks then with physical therapy usually does not re-dislocate. It anything the problem after dislocation is stiffness. But if full range of motion is attempted too early or the ligaments do not heal or if there an associated fracture it can dislocate again..