That’s rough! Some members have had GI issues, it can be caused by vagus nerve irritation, and the swallowing issues could be from the glossopharyngeal nerve which is commonly affected by ES…Some members have had swallow tests done- usually because of pain & difficulty swallowing, one of the ‘hoops’ doctors make people go through before accepting it could be due to ES. But that might be worth having done in your case? One of our members with hyoid bone issues also mentioned this cricopharyngeal spasm, but I don’t know really how you can differentiate between this & ES causing nerve then swallowing issues. Here’s info:
Cricopharyngeal Spasm (CPS): A Feeling of “A Lump” in the Throat
If you search for acid reflux it’ll come up with quite a few discussions, not that there are many answers, but at least you’ll see you’re not alone.
This discussion is also helpful as @GrnyAny explains how badly her vagus nerve affected her:
Successful Surgery for severe Vagus Nerve Compression - General / Eagle Syndrome Stories - Living with Eagle
I hope that you’re able to find some other options for liquid medication 
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