Steve

The exercise you describe is called the Shaker Head Raise. It is the most basic of all rehabilitative swallowing techniques. You should master it in a week with some work.
My advice is to get your doctor to write a prescription ASAP for speech therapy and then make an appointment with a SLP (speech language pathologist) who has swallowing experience.
I know it sounds funny to get "speech" therapy when what you want is "swallowing' therapy but in one of those medical quirks, SLPs are the best at swallowing therapy.
Here's a peek at the exercises in store for you
Rehabilitative Swallowing exercises

Most people do regain their swallowing, so go for it.
Mine was an exceptionally complex and unfortunate situation
Charm