Embarrassment at crying in front of someone is itself good material to work with, especially if it is intense. Behind it there is usually a rule learned early: that tears are a nuisance, a weakness, or that someone important got upset when they appeared.
A few things worth knowing:
It does not need stopping. The reflex to pull yourself together fast is exactly what you do in the rest of your life. The consulting room is one of the few places where it is not necessary, and forcing a stop often interrupts precisely what had started to surface.
It does not need explaining. “I don't know why I'm crying” is common and is information in itself — the body reached something before the words did.
It is not a measure of progress. In neither direction. Some people cry every session and nothing changes; others never cry and do deep work. Crying is neither compulsory nor a sign things are going well.
Its absence is not a bad sign either. Someone who cannot cry at all, despite feeling there is reason to, is usually describing something else — a regulation mechanism stuck in the off position. That too is workable, but it is a different thing.
What happens practically: the therapist will not rush and will not change the subject to get you out of the situation. They will wait. And if you are still shaken at the end of the session, it is part of their job to help you settle before you walk out of the door — if that does not happen, it is worth saying.