“The hug” is not a medically recognized term anyway, and is often described in different ways by different people. People quite often talk about a feeling of pressure, or constriction - as if they couldn’t breath (hence the nickname “hug”). What people mean when they talk about “the hug” is actually a spasm of the tiny muscles between the ribs (intercostal muscles). As these are what let your ribcage expand and contract flexibly to accommodate your breathing, then if they go into spasm, it will make breathing feel more difficult or painful.
It’s not clear from your description whether this is definitely what you experienced. It could have been a spasm of the intercostal muscles, it could have been some other MS-related muscle spasm, or it could have been nerve pain that was not related to a spasm at all. And without wishing to worry you, there’s always an outside chance it might not have been anything to do with MS.
If this is completely new to you, I suggest you mention it to your GP, and not just take bets on it being “the hug”.
I do get an indigestion-like chest pain under my breast-bone, which I think is my personal version of “the hug”. The reason I am fairly confident of this, and that it’s not anything worse, is that it responds to muscle relaxants like baclofen and diazepam. therefore I feel I can be fairly certain it’s a muscle-spasm of some sort, and that’s why muscle relaxants help. It doesn’t sound as painful as you describe, though, and that’s why I would be cautious of assuming its the same thing.
If you happen to be on any muscle-relaxants anyway, did they help, or make no difference? Obviously, if you’re not on any, you will not have been able to try this experiment.