As others have said, you don't need to apologise but it might be helpful for your T to know how you are feeling.

Just because you're not talking, doesn't mean you aren't saying anything. Much of the way we communicate is non-verbal. And I think it can be misleading the way people talk about therapy as 'the talking cure' or 'talking cure' when it doesn't have to involve talking.

It sounds like emailing might help you. Also, try to remember that - given how anxious you feel - you are doing so well to get yourself to therapy in the first place. That's an achievement in itself. Your T will know that too.