Maybe explaining to the student health service that you've already been diagnosed with MS, that you're in the middle of a flare, that you need to see a neurologist, and that an MRI alone won't help, will light a fire under them.
If you've already picked out the neurologist that you're going to switch to, call the office, and explain to them that you're in the middle of a flare - hopefully they would be able to squeeze you in. In the meantime, ask them to let you know if they have any cancellations (or if they won't do this, keep calling them). When I was first experiencing symptoms of MS, this is how I got in to see a neurologist quickly when he had a 2 month wait. I know this is a pain when, especially when you're dealing with MS, but sometimes the squeaky wheel....
Of course, if the symptoms of your flare-up are bad, then the ER may be a consideration, if, for nothing else, to rule out another cause.