Hi and welcome. Kudos for being honest- I know it's only here but hey, it's a start

I think you really should tell your T about that- if she's a good T she'll see it for what it is - a progress, yeah! and be happy for it. - that's the great thing about Ts, it's about YOU and not (well, should not) be about their feelings.
I think telling lies is one of many important social skills, nothing to be ashamed of. However, telling the truth feels so much better, it's freeing though it requires a level of safety and trust in the RS. Starting with your T is a great idea, hopefully one day you'll be able to be more honest with your friends/family.
I do think you're too hard on yourself and it's not helping the situation one bit:/

Btw Yes, fake memories, if repeated long enough, can feel real esp if you're working with them in therapy.