Hiding my true emotions became habitual for me early on. Mostly this was due to fear of disapproval; and/or worse. That was rather contradictory, I now realize, in that I was considered worthless, that no matter what emotions I dared to have were automatically disapproved of.
On the one hand, I was hypervigilant; inside, I was grieving and furious at this state of affairs. This also happened frequently at a private school where I ran the risk risk of disapproval for even the silliest of reasons. I learned the game but at the risk of losing my sense of self. Why? Fear -- so I learned the ways I thought would win approval despite the odds. Which of course increased the sadness. Nothing worked, and I took in further the notion that I didn't matter; that hiding my true emotions might help (it didn't!).
Had I been honest, the consequences were too fearful to contemplate. Nowadays there's a huge difference -- I'm not trapped back there in the FOO or in that travesty of a school.
I'm free to be who I am. It's taken a while for me to catch hold of my habit.
Which leaves me with just one suggestion -- to be honest with oneself at all times. Those people I had to please (or so I thought) are long gone from my life. It sounds easy, eh? It surely hasn't been, as the other part of the process is I still fear the consequences of others, no matter who they are.
You've taken a first step, though; which is just the self-realization that you're prone to this. If you trust your T enough, just try and be as honest about your deepest reactions to what you're discussing. If your T has already mentioned this, and there's trust between you, you might find it freeing to react from your heart, and not the mask that's become habitual.
I know that's helped with my own T, but it took loads of trust before I felt bold enough to loosen the mask, and finally let it drop, at least in that relationship. At our most recent session, she took pains to note that I can now speak more easily in my authentic voice that is more willing to share from the heart.