@Gin
Well everything you say does not point to Meniere's disease exclusively. Could be as you said migraines, allergies, or Lyme disease. Sometimes chiari malformations or abnormalities with intracranial pressure can do those things too, but given that you have been to a neurologist and had an MRI they probably ruled those out based on test results and symptom history.
Have you been put on a migraine diet or have you tried to search for triggers/allergens in your diet? That's also a good place to start just in case your body has any sensitivities (i.e. gluten intolerance).
There are two other things I can think of. One is a perilymph fistula; but that is only possible if you visibly remember having an injury (pressure, really loud noise, physical) to the ear affected by Meniere's disease. The other is, as you thought of, lyme disease. The facial numbness is kinda raising red flags for me. I just found out I have Lyme disease, and Bell's Palsy and facial numbness can go hand in hand with lyme in the absence of other neurological explanations (and yes the MS, brain tumors, Parkinson's, were ruled out for now if your MRI and CT scans were clean).
About a year ago, I had some weird facial numbness symptoms and spells of facial neuralgia, which I thought were due to compacted wisdom teeth and my nerves being destroyed by loud bass music; in hindsight these symptoms were the beginnings of my lyme infection.
And Lyme disease does go after the inner ears; I know that first hand though as my ears are always on fire and my hearing is always changing from the slightest environmental disturbances or bodily movements. How it attacks the inner ears is something that I don't think science has come to understand yet, but I wouldn't be surprised if it produces Menieres-like symptoms. For me at least, I think either the lyme or one of the co-infections has gummed up my micro-circulation around my inner ears, as my ears are set on fire whenever blood pressure is altered suddenly.
As a word of note physicians and neurologists easily overlook lyme if just one of the tests they give you comes back negative; some Lyme tests are better than others, but all of them have a high false negative rate. To really know the truth you need to find a
lyme literate doctor in your area, because they know whether it is lyme or not based on your symptomology and can conduct a far greater number of blood tests specific to the illness.
This avenue should, of course, be pursued if you have been in a region known to have ticks carrying Lyme disease (sorry, too lazy to look through details about where you are from).
Other than doing that, all I can suggest is to do any diet modification work and coordinate any with your neurologist who is treating you for the migraines, if you haven't already.
I'm really sorry that I cannot think of a different migraine med you should try. Consult with your neurologist about one with fewer side effects. All I can tell you is that you most likely want to avoid the topomax.
Hope any of this helped!