I also have Lyme with neurological involvement as evidenced by MRI. I have been treating for just under 2 years and am much improved, but can still suffer set backs and flares.
I can only speak from personal experience, but when my body is under any extra stress (such as from a common cold), my Lyme symptoms do flare. It makes sense to me in that a cold will trigger an extra immune response, and so that will also affect any low lying chronic infections.
I've experienced a flare from a cold specifically, but also other events can trigger them, as well. In my case, a deep tissue massage once sent me into a "flare" of sorts, during which my cognitive issues returned and I had obvious symptoms of high systemic inflammation. Stress, travel, and extra work are all more difficult for me to juggle since my Lyme disease. My heat intolerance has improved with treatment, but at times getting too hot could exacerbate my symptoms terribly to the extent that a hot shower once left me bed ridden for days.
There is a lot of overlap between MS and Lyme symptoms, and some theorize that Lyme may even trigger MS (since the cause of MS is still not well understood). While MS has a very different prognosis, Lyme can actually cause *more* symptoms than MS, because MS attacks the central nervous system while Lyme is systemic and can affect the nerves, skin, heart, joints, ...
Therefore, a "red flag" that Lyme is the culprit and not MS may be if you experience joint pain in addition to your neuro symptoms. Also, Lyme can really irritate the peripheral nerves, and cause transient symptoms (like tingling and buzzing that can move around in your body). In MS, lesions in specific locations cause symptoms in specific areas, so the tingling and other "paresthesias" experienced by MS patients will be in the same place (like a patch on your left leg, as opposed to up and down the whole leg). Also, because of the asymmetry in newly formed lesions, MS symptoms rarely onset in a bilateral pattern. For example, a sudden onset of tingling in both right and left hands is more suspicious for a systemic illness like Lyme than for MS.
(I was never diagnosed with MS, but it was the top of my differential diagnosis for a time due to the brain lesions, and at the onset of my illness I was in a top MS demographic [caucasian female near 30]. My Lyme tests were mostly all negative, too. It took about a year and a lot of persistence to get treatment for Lyme, and even I was skeptical at first but I had such an obvious response to the antibiotics that I eventually became convinced.)
By the way, there is also an active MS forum on MedHelp,
http://www.medhelp.org/forums/Multiple-Sclerosis/show/41
My opinion (note I have zero medical training!) is that if you experienced Herxheimer reactions followed by improvement from antibiotics, then I would pursue further Lyme treatment. There is no cure for MS, only expensive and difficult disease modifying drugs that may or may not slow progression. To my knowledge, there is no conflict between most MS treatments and Lyme treatment through antibiotics.
Sorry to carry on, and best of luck.