I cry in front of my T all the time, so I can't help you with advice from my perspective. But I'm wondering--is it partly that you fear your T will be looking at you when you cry? If you feel like the tears could possibly be coming, could you ask your T to look away? Or else maybe hold something in front of your face so your T can't see, whether your hands, a pillow, blanket, piece of paper, whatever?

Another thought is to go back and examine with your T what made you feel unable to cry as a child. Did your parents teach you to keep emotions inside? Did you fear punishment or ridicule (by them or by others in your life) if you cried? Did you feel you just had to hold it together for some other reason? If you can go back to how you felt then, maybe it could help you now? And maybe it could help your T reassure you that whatever it is won't happen now?