First, take a DEEP breath. If you DO have MS (and it's really much too early to tell!) that doesn't mean all that much with regard to your kids. You'll likely be around a long time -- I've had MS for 25 years, now, I'm 61 -- so set that worry aside.
There's a lot going on with you -- at age 44, having a new baby, a history of other neurological problems in your family (the brain tumor, the pituitary thing..). Make sure you tell the neuro all that when you see him.
You may not actually see a neuro tomorrow -- so don't be disappointed if indeed you have to wait awhile. Did your doctor offer any suggestions about which neuro to see, or offer to refer you to someone? Usually a doctor's referral will get you in to a doctor much more quickly than you simply calling an office. You might want to call your doctor back and ask for assistance, so yo u don't have to wait a really long time to be seen.
The neuro will want a complete family history, so while you have some time now, write down everything you can about your health history, and gather up your records, including the new stuff. Make sure your rheumatologist knows you're seeing a neuro, and have him forward any records he might have, too. And indeed take the MRI and any written results from that (or have your doctor forward them for you.)
What your rheumatologist did sounds much like what you'll get at the neuro's office -- a test of your balance, sensory testing (pins pricking you to see if you can feel them), strength tests, other things. He may do a series of blood tests to rule out other things (if your primary care doctor hasn't already done that..and sent along his records). He'll want that medical history, and will ask about your pregnancies (and if you had any health issues after the first three).
All this may take awhile, so you'll not get answers right away anyway. Just hang in there, come back with questions, love your kids, and give that new baby a hug from us here! :)