How do I convince him that I have ME ?
I probably have a different philosophy than most but I would not go to the appt trying to convince the doctor that you have ME. I would tell him all of your symptoms and see what direction he goes with testing so you can try to rule out if something else is going on (either a missed diagnosis or a co-occurring diagnosis) as many of us have multiple medical problems.
He will probably do standard autoimmune testing (ANA, inflammation, and basic autoantibodies) and if there are specific tests that you feel would be useful based on your symptoms, I would ask for those tests.