You probably don't need to apologize, but you could certainly tell your T that you feel like you need to apologize and explain why.

I struggle with this, because I feel like I need to apologize for everything, including just existing, so I've started checking with my T. I'll email or say "I feel like I should apologize, but I'm not sure if it's necessary" and then explain what I'm thinking. My T will often talk about it with me and help me figure out if an apology is really warranted or not. In almost 6 years, she's only said that an apology was probably warranted twice. I, on the other hand, feel like I need to apologize to her nearly every session.