Yes it does sound like anxiety. Lets not forget that M.S. can cause anxiety and depression....not that the disease makes us anxious and depressed (although it can) but it also can cause them.

I developed these types of symptoms years ago and they were out of the blue. They got worse very quickly and I also started getting phobias I never had before also.

After awhile they lightened considerably. I still had some issues and the doctor had me try Celexa (antidepressant) which has properties for anxiety, OCD, phobia etc. It really helped.

Learn to deep breath properly and you may be able to get through these episodes rather easily. Don't become afraid of it or you may set yourself up for even more anxiety.
Note: Let your doctor know about these "feelings" to make sure other things are not going on (hormones, cardiac etc)