What type of doctor did you see? It is important to see a doctor who is familiar with throwing problems. Cortisone can provide temporary relief of pain from inflammation but it does tend to weaken tendons and ligaments when overused and it won't heal the source of the problem unless knocking out the inflammation is enough to let it heal. In any case, a doctor has to prescribe the cortisone shot so the doctor is the person to talk to.
Not all UCL problems can be picked up from an MRI. There are also nerve problems such as pronator syndrome that many doctors will miss.
BTW, I don't know if it is true, but I've heard that the area around the cortisone shot will be pretty sore for a day or two afterwards.