Do you even have probs with your digestive system? Bloated feeling, sharp pains (especially left above your navel or up and down your oesophagus), nausea? Pain in your stomach when you lay down? Sores / ulcers in your mouth?
Becasuse it's very easy to just say, this is your digestive system. It's something soooo common (plus the imuran gives you more acid). And easy peasy, just give them 3 months omeprazole and you're done.

What is the reason you need to drink while you eat? Will you choke if you don't? Will it just hang there uncomfortabally, will it go through your nose?
Do you have any other weakness, like chewing or laughing?

Of course it's very possible it's your digestive system, but swallowing problems when you have MG is definitly something they need to take a look at.

When did you start your stomach meds? Because they do not work immediatly if you have an ulcer, this can take weeks, sometimes even months.

Anyway, I find Abby's thoughts something to consider also!