As with what Daisy said, A good key to overcoming some of that fear is to take drinks with every bite if you have to. especially when you have a dry mouth, it might feel pretty rough going down, but the esophagus is very strong and very good at forcing food down. You'd be amazed at what some people successfully swallow. I've always wondered about the whole food in lung thing. It's got to be highly unlikely... I'm pretty sure (And I'm no doctor so don't judge) but the epiglottis functions to keep food going in the right direction. a function that can't be failed. You get food in the wrong pipe, you cough it up. You'd be amazed with the power of your body.
I have that fear sometimes when swallowing pills or vitamins, I feel that it's lodged in my throat. If you cough quite a bit, you might feel a lump or that you have an obstruction.. I've noticed that if I irritate my uvula, it will get to the point where I can actually flip it up onto the back of my tongue, which is super annoying.
I hope all is well, keep hydrated... Drink water and get comfortable with it. There's nothing that can stop the force of water.