Therapist believes I have autism but I'm unsure

My Cognitive Behavioural Therapist, who works with autistic adults frequently, has said that she believes I have autism. I've been going to her for a while now (around 5 months) and the topic of autism hasn't been brought up before this, but she believes a few things I mentioned in my last session with her has put a few "pieces of the puzzle" together regarding my mental health, and has led her to believe that I have it and that I should arrange to see a psychiatrist.

Honestly, her saying that she believes I have autism was a relief -- I don't feel as though I've ever fit into the boxes people apply to mental health issues such as social anxiety and generalised anxiety, and the way she explained it to me, I could definitely see how it related to me. To put it briefly, the way she explained it to me was that the people who have "regular" anxiety issues won't have a good grasp on what would make them feel better, and then understanding that eventually helps subside the anxiety. I've always known what will make me feel better (in my first session with her I explained that if everyone just understood how my anxiety affected me, I probably wouldn't have anxiety) and exactly why others would perceive my anxieties as "irrational", but knowing that doesn't help me.

So I felt relief after listening to the ways she described the autism spectrum, because for a long time I've just felt that this constant feeling of apprehension, anxiety and distress I have from doing things a regular way that are out of my control was just something that I had that I wouldn't be able to put my finger on. 

But now I've come back and started to research it, and so many of the big signifiers of autism just don't apply to me at all. I've never had issues with eye contact, the apparent telltale signs of a child with autism such as not playing with others, repetitive playing, etc. don't fit me, and stuff like delayed language skills and not knowing how to "pretend" in play couldn't be further from the truth.

I know autism is a spectrum, but when YouTubing high-functioning autism and seeing other people with it, I couldn't relate to a lot of what they were saying. There was always some caveat that "very few people with autism won't have ever struggled with X," but I just think what are the odds that I fit in this box. But then I also think that there may be plenty of people like me, who can't put their finger on while they feel so much discomfort and distress but not to the point where it's debilitating enough to do something about it, so maybe there aren't many people on this side of the spectrum who speak up?

I just wanted some opinions and advice here, and to hopefully find someone who may be in the same boat as I am with this.