They used to call it the "girdle", and I think that described the sensation better then the "hug". It is like a very wide elastic stretched to the max, wrapped around a person, then released to synch them up tight around the middle.
As per the link Cheryl posted, "It is caused by a lesion on the spinal cord" and "is technically classified as a neuropathic pain called a “paresthesia,” which refers to any abormal sensation". Some "abnormal sensations" we get with MS include:
"Paraesthesia describes a number of abnormal sensations just about anywhere in the body. These include tingling, prickling, pins and needles, electrical-type buzzing, burning, skin crawling, itching, partial numbness (like feeling through tent-cloth) and a variety of neuropathic pains."
http://www.mult-sclerosis.org/paraesthesia.html
When I had the hug, I had ALL of those sensations combined with a feeling like I was swollen. I also had severe sensitivity to touch, as if someone was scrubbing me with a SOS pad when they slightly brushed my skin.
I have had a heaviness in the chest too, with "apparent" difficulty breathing, but had a COPD test and all was fine.

This occurred at the end of a spinal lesion attack, after all the other "hug" sensations went away.
I don't know if we really have a satisfactory description of what the "hug" is. What has me a bit stumped about your explanation is that pain relievers do not usually help at all (or very, very little) for neuropathic pain.
If it were me, I'd be considering GERD or something like that instead.
Cherie
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