I don't think this is an embarrassing question or anything you should feel ashamed of posting
While I don't have heavy periods myself, I know a few women who do, and they say that they have switched over the diva/moon cup because it holds a lot more of the flow for a longer time period (12hrs or so), versus pads/tampons that need to constantly be changed because of saturation. If you prefer to stick to pads/tampons: double up. Wear a tampon of the highest absorbency and pad. That way at least if the tampon leaks before you can get to it, you have a back=up!
Is it possible to go on the pill to decrease the heaviness, or possibly go on a specific pill to stop periods from happening except for only a few times/year?
Good luck. Sorry about the white uniform. What a ridiculous idea in a mostly female profession.