The fear that you're not 'real' is very common and pretty scary to face. Fear that's scary, who would have thought?
But here's the thing... there's not a test or a set of prerequisites you have to meet to be trans etc. Our society heavily scrutinizes us and is always trying to find ways to invalidate us. Unfortunately, most all of us have, to some extent, internalized those feelings to the point of them feeling like our own feelings.
If a therapist doesn't believe you, then they are probably wrong and judging you with their own bias. In that case, you should look for another one because professionals or not, they are still subject to their own views. I really don't believe you will run into that issue though, especially if you find a gender therapist specifically. Either way, your truth does not change.