Any therapist worth their salt will not be fazed by a client crying.

Hell I was in a facility years ago where the client with the therapist in the room next door to me and my therapist, that client would have severe anger outbursts and start yelling like crazy. But she was back every other week with him (the therapist) and my therapist and I would hear it coming through the wall and be like O_O and then have a small chuckle.

So don't worry about some crying, unless your therapist totally sucks they will not suddenly dump you as a client just because you cried, that would be insane.