swallowing difficulties afflicts people with MS, you might try posting there too, to see if you get a response, I have trouble swallowing but embarrassment in front of coworkers is not a problem. And I get things stuck in my throat, like medications. There are good reasons why pills are enclosed in casings. I haven't met one that tasted like mint yet.
I try to sit erect, and tilt my head back to straighten out my throat. That seems to work. Also the glass of water to flood everything down. There are all sorts of tricks. A physical therapist can help you with those, also speech therapists know a lot about swallowing. You might have a friend who is trained in those careers to ask.