Welcome--Now, I have no idea what kind of training an aspiring fitness competitor such as yourself might be doing but I think it's wonderful you're pursuing it.
That said, with respect to the Avonex, I've read that some people find the "mix it yourself" results in far fewer side effects than the prefilled syringes. If you're using the prefilled syringes maybe you want to consider switching to the "mix it yourself" version.
With respect to the "core body temperature", if you're in the US, you could check out the MSAA Cooling Program
and see if there's some equipment that might help keep your temp down when your exercising. It's free to people with MS.
The fitness center where I exercise has fans (in addition to the AC) and I've found they help me a lot.
Hopefully others will have some ideas. We'll be waiting to hear how you do in the open competition. Wishing you the best with it--