I also have MS and take Rebif for it. I have a small case with room for the auto injector, prefilled syringes, alcohol wipes, etc. It also has a section for the freeze-able pack that came with the kit to keep the meds cold. The first time I had to go through airport security with it was in June, and I had NO problems with it. In fact, I was pulled to the side so they could hand search my carry on, and I thought it was for the pack. The TSA guy said "No, that stuff's fine" and kep looking. He finally found a tiny swiss-army knife that I forgot I had at the bottom of a bag in my purse, and confiscated it!

But they didn't look twice at the syringes.
Most recently, in October, was equally as easy. The airport had papers so you could "declare" any liquid medications, and I threw the whole pack in one of the plastic baggies for good measure, but they didn't say anything about it. I think they're used to seeing that type of stuff.
At the most, I would be sure to have your prescription (or note from doctor) with your name and the info about the meds with the medication, just in case. And the resorts on property will give you a fridge to keep it in, no probs.