The symptoms, causes, and effects of milk intolerance are very varied, and can be misleading and confusing. I assume that the medical professionals you deal with know that perfectly well. Most of the people that I have run across that are terribly confident about purification, herbal treatments and so on soon make it clear that they really don't know what they are talking about. (For instance, to speak of lactose intolerance as "milk allergy" is a frequent dead give-away!)
So I won't pretend to be an expert on the matter, because I am not. Anyway, trying to sort out symptoms at long range is a very chancy business!
However, I assume that you have been tested for both lactase deficiency and other causes of milk intolerance, such as indeed milk protein allergy (which can occur either independently or together.) Some symptoms can be a secondary result of lactase insuffiency. For example, apart from gassiness and cramps, gut bacteria may produce irritant compounds when they break down lactose in the gut, and some of those compounds might produce dizziness. This would be consistent with some of the effects, but as you can tell, I am speculating.
On the subject of blood-brain barrier, this is a simpler matter in concept at least.
Yes, there is indeed a barrier. In a healthy person it is very choosy about the compounds that it permits to pass through. Very few germs and germ products can get through, and not many of the products of metabolism that we normally find in our blood.
However, that very barrier can be a real nuisance when we need to get say, antibiotics into the brain. Many of the most useful products cannot get across it. It is not as simple as just bad things being unable to cross, and good things being persona grata. Also in some disease conditions the barrier may become leaky, permitting harmful substances to cross.
At the same time, if nothing at all could get through, the brain could neither get the necessary food, including oxygen, from the blood, nor permit the blood to carry away waste products such as CO2. More or less in consequence, there is no magic to the barrier. It cannot always tell whether a particular molecule would be good or bad to let through. Various substances, including small molecules like ethanol, can in fact cross the barrier, which is an important fact in the matter of the effects of strong drink on the brain. Some typical gut fermentation products of lactose, such as short chain fatty acids and 2,3butanediol get absorbed into the blood, and they can cross the barrier and might well have an effect such as dizziness.Some people suffer migraine in reaction to such compounds. This is not necessarily from lactose fermentation though; it can result from sudden dieting causing fatty acid mobilisation from their fat stores into their blood.
Notice however, that if such products were responsible for some of your experiences, then you probably would be especially vulnerable to them, because they also occur in various quantities in other people's guts.
I think that covers your specific questions, but I am sorry that what I could tell you probably is too vague to be of much value.