The balance organs are in the ears, so I don’t think it’s just random coincidence, or something you’re imagining. Ear infections sometimes cause problems with balance.
But I’m less sure whether it has anything to do with MS. Obviously, you should not normally get dizzy just from using earplugs, or they wouldn’t be marketed as safe. Perhaps you should ask your GP to check your ears, just in case there’s anything untoward, such as an infection you’re unaware of?
Yes, MS can mess with balance, of course - it’s something many of us are aware of. But as it’s only when you use the earplugs, I wonder if it’s something much more straightforward?