Growing up as a very sensitive girl, I was shamed some as well about emotion - not as much as boys are to be sure, but made to feel like it was somehow unseemly. After I started doing healing and growth work in my mid-40s I finally got over that. Now, if I tear up in a restaurant or whatever, I just let it be. It's other people's issue if they don't like it.
I remember reading something years ago about this man who was somewhere pursuing healing and wisdom - maybe with some sort of monks. He said he cried almost non-stop the first two days, just letting out all the stuff that he'd suppressed for decades. He very much agreed with you that it was cleansing and therapeutic to just do this as needed. I wish our culture supported that more - particularly for guys.