I have had a lot of the same problems as you have, bad guts related to wheat (not coeliac) but since being on a paleolithic diet no probs with my gut and more energy, dizzy spells, visual problems, numbness, pins and needles, breathing problems, crushing exhaustion, burning legs, trouble walking, ok for long spells then feeling like I have been in a car crash.
Well I have been going to the doc's complaining for years (since 1974) and have seen many consultants, had blood tests and x-rays, dye put into my spine and x-rayed plus loads of other test all with no firm diagnosis, not one of them twigged or had any idea. Then in 2006 I was sent to see a spinal consultant at Nottingham QMC who did all the usual x-rays again but then sent me for a MRI on which they spotted lesions on my brain and spinal cord so was finally diagnosed with MS.
I have no gripe with the consultants that missed it, it is a sneaky little bastid and most doc's don't see it, even Neurologist have a hard time diagnosing it and I was probably better of not knowing as I just got on with my life.
I do hope you haven't got it but then again there are worse things to have. I have made changes and am now much better. I eat what humans evolved to eat, drink clean water and get plenty of sleep, work full time and build comp safari motors

So what ever you have I hope you get a diagnosis soon and there is some positive action you can take to make thing better.