Okay… Resident pee shy sufferer and overcomer here.
It was so bad when I was a child that my first grade teacher called my mom to tell her she was really worried about me because I never used the bathroom at school.
In middle school I would squeeze the milk out of my cereal before eating it so I would be so dehydrated I wouldn't need the bathroom, all though high school.
How I got over it:
I started stomping a bit, or bringing a backpack with my and making a big deal of unzipping the zippers so I could start peeing. Making any noise that is totally normal in a bathroom stall and pushing as hard as I could to pee during it. Once you start it's usually auch a relief that you keep going after that hurdle.
You can also cough or clear your throat but sometimes that would make me nervous personally. It also helps to take deep breaths, but honestly nothing worked better for me than rustling my bag personally. It's also important to do this immediately upon sitting down, the longer you sit the harder it will be.
Good luck, nona, I was convinced I would never fix this. I'm not perfect, I still avoid peeing in public but at least I /can/ if I really have to.