It sounds to me like she does believe you and even said so. She said, "There is no reason not to believe you."
You are looking specifically for the words, "I believe you" and because you did not get that, some paranoia is happening. You are using negative filtering where you are catching only the negative things (therapist did not actually say she believes me) and not catching the positives (therapist listened, took me seriously, said there was no reason not to believe me, and understood how being believed is important to me.)
So, I totally do this too, and you gotta call it out on yourself.
Also, you are mind reading and this can fuel more paranoid thoughts which can increase worry and insecurity.
Call that out too. You don't know what your T really thinks. That sucks, I know.
You can use Wise Mind. What does your gut instinct tell you? Do you feel believed?
Or are you worrying over this and second guessing her sentences really because you most likely have had other people not believe you in the past? Our fears and worrys can take hold so much that we believe them so much and we see signs of them happening in people. Your worry is a sign as to how important feeling believed is to you. But your worries and interpretations are just that-worries, opinions in your brain.
In therapy it is easy to project harm that was done to us on our T.
Perhaps you were not believed before?
It seems to me that your T gets this, believes you, and knows how important this is to you.
But then again I am only basing this off of what you wrote.
Can you use your wise mind?
Can you check the facts? How many times in the course of your treatment has your T believed you?