It probably won't always be like this. If you're concerned over how much you're crying, maybe you could talk about that in therapy?

Sometimes our emotions need to come out, and maybe being in therapy feels safe enough for you to let go of some control and be able to cry.

You are completely and totally normal. I've left many sessions after crying a lot, and yeah they do affect the entire day a lot of the time! (That's why I like later in the day appointments, less stuff to affect!)

I'd say she's getting to know you, and that she sounds like a good therapist and someone you need right now. So I don't advise quitting therapy! Finding a good therapist and creating a safe relationship takes a lot of work - and it sounds like this therapist is exactly what is good for you right now.