Often even when I trust my therapist and want to be able to say something, the shame and anxiety can make it very difficult to actually do so.

I think the things I'm still holding back are a matter of trust though. I don't completely trust that my therapist will be willing and able to handle that stuff, and I fear rejection or judgement and further shame.
If I somehow knew with certainty or learned that it was something he'd handled before and was okay with handling then I think I'd be able to tell him, though even if I trusted that he could handle all the details I think I'd struggle to disclose those.

I've been seeing this therapist weekly for a few months. But I've opened up to him far more than I have to other therapists whom I saw for years. I think it's both him and the attitude with which I approached therapy this time. I was determined to actually be honest and try to work on things, and made a commitment to myself not to tell any outright lies (though I totally use lies of omission).
I did lie to him 2 sessions ago out of instinct/habit, but then this past session I started it by telling him I lied and what the lie was, and that I was not ready/willing to discuss that topic further, but that I should have just said that rather than lying. That was really hard to do, but he responded well.