None of the standard treatments for MS (Avonex, Betaseron, Rebif, Copaxone) lowers your immune system. They alter your immune system. MS is a disorder of the immune system, after all: your immune system, which is the system that "attacks foreign invaders" like bacteria and viruses, killing them off -- is attacking your myelin. That's what causes the lesions. So the drugs try to "train" the immune system to recognize your myelin as your myelin, and stop attacking it.
So you don't want to take any of the meds that are out there to fight colds and flu that claim to "speed up" your immune system.
But you definately want to get the flu shot, if you haven't already, and a pneumonia vaccine (this vaccine is good for a number of years..I think 10..so it's a one-time shot). And you want to get the flu shot every year, as the flu strain changes every year.
While getting the flu shot isn't a guarantee that you won't get the flu...it does improve your chances of not getting it. Or if you do, it'll be mild.
We with MS don't want to subject ourselves to anything (like the flu, or pneumonia) that increases our body temperature...gives us a fever...as that can make MS symptoms worse, for the duration of the fever.
You can go to the National MS webpage and read their recommendations -- which strongly enourage folks with MS to get these shots.
...I am not a doctor, nor health professional, and don't pretend to be one, here.....