Hi and welcome. Sorry to hear that you have MS, but it doesn't mean you have to change your life (necessarily). Swallowing problems can definitely be caused by MS. Your Neurologist will probably order a swallowing test where they image you while swallowing. They can determine any abnormalites in the reflex itself, and mechanical issues which could potentially cause a choking hazard. It's a simple test - I had it years ago - and is often performed by a GI lab.
If your difficulty is esophageal - you'd want to see a gastroenterologist. I was lucky enough to have both - but I'm special that way, lol. I wish you the best figuring it out. It's an essential skill - swallowing!
Have you started any treatment with disease modifying drugs? I wasn't able to tolerate them, so stopped them months after my dx. I've had MS for 20 years - so have read about everything there is on the subject - lived the rest. I have Secondary progressive MS now, and am having the most significant disability now. MS was pretty easy for me, other than occasional flairs and foot drop, for the first 15 years.
Hopefully you will have a relatively "benign" course. But everyone has a unique journey - with some similarities of symptoms. Did you get a thorough explanation of your MRI and clinical analysis by your neuro? Did he/she say it was RRMS? I truly believe having a good doctor is important. I hope this was in some way helpful. You can look up the symptoms and tests for swallowing on the net. Let me know if you have specific questions aboug it. Blessings, Jan