If you came to see me with this information, I would widen the scope of your assessment to include the cervical spine, thoracic spine and shoulder function. I may even leave your elbows alone for a little while (partly a decision to avoid too much focus on pain as this increases any neural sensitivity). I may try mobilising the cervical spine, loosening up the cervical muscles, doing a lot of work on shoulder stability and working on the muscle balances around the shoulder girdle.
If your physio hasn't done the neural provocations tests that Roycar suggested then I would suggest that you find a physio that will do these (someone who has done the NOI courses for example) That being said they will probably all be positive from what you have described. But I would plan treatment by observing if there is any change in the neural provocation tests with a treatment to your neck.
In the meantime you should avoid any activities that aggravate the pain. if there are any positions that relieve the pain such as leaving your hand on your head for 5 minutes then you should do this whenever you can.