I'm sorry you are in this situation. It's weird and scary when you realise that something that feels safe and comforting could actually be a bad thing.
And I would say that not just the cuddling, but also the fact that the therapist asked you to come by for a chat outside of your normal session time (if I understood that correctly), and that you have ongoing txt message conversations about friend-type subjects, are red flags. I'm sorry - I understand that these are very comforting things. But a therapist's job is not to comfort us, and there is a good reason why therapy is not a kind of friendship.