I do not think the iron would act so quickly. That is, if it is related to the iron, it could have been slowly building until it reached a tipping point.
the flu is an assault on your immune system and sometimes the assault damages or "weakest links". In your case, the flu you experienced could have been your tipping point. The good news is that you are on top of the situation and making the right moves, I think. Just so that you make sure- a neurologist can be a "jack of all trades" (general neurology) or a specialist (MS Specialist, Parkinson's Specialist, ALS Specialist.....). If MS is a possibility, I would encourage you to start with the MS Specialist and then have them refer you to another specialist if needed.