Thanks for using the forum. I am happy to address your questions, and my answer will be based on the information you provided here. Please make sure you recognize that this forum is for educational purposes only, and it does not substitute for a formal office visit with your doctor.
Without the ability to examine you and obtain a history, I can not tell you what the exact cause of your symptoms is. However I will try to provide you with some useful information.
I am not sure what you mean by the term dizziness. When some people use the term dizziness, they often mean vertigo, or room-spinning. Others mean a light-headed, whoozy feeling.
Your symptoms as described above may be consistent with a variant of migraine called basilar migraine. Basically this is marked by several hours of vertigo associated with nausea, light-sensitivity, and sometimes other symptoms. Headache may or may not be present. The treatment is different from that used to treat other migraine types; the treatment in this case is a type of medication called calcium channel blocker, such as verapamil, which is actually used to treat blood pressure but works in type of basilar migraine as well. Sometimes, migraine disorders can cause some changes on MRI, just small white spots, that are of no clinical consequence. Nonpsecific foci on the MRI that you describe can be due to migraine or due to changes that occur with vascular damage, such as occurs in people who smoke or have hypertension.
If by dizziness you mean vertigo (room-spinning), the causes could be either the inner ear or the brain. Inner ear causes of vertigo most commonly include benign positional vertigo (BPPV), which is due to small particle in the inner ear that moves out of place, and can be repositioned with simple head maneuvers. The symptoms often include vertigo that occurs with turning of the head, often while turning over in bed. Another cause, if your symptoms are associated with tinnitus (ear ringing) and hearing loss is called Meniere’s disease and can be treated with medications and sometimes surgery. And so on, several other causes from inner ear problems exist.
Vertigo can also be due to problems in the brain. The most common is a benign tumor called a schwanoma (also called acoustic neuroma). This is diagnosed by MRI of the brain, and since your MRI only showed a few nonspecific foci, this means there is no tumor. Multiple sclerosis can cause vertigo, but often, other symptoms are present as well. A normal MRI of the brain excludes multiple sclerosis; the description you provide of your MRI does not suggest MS. Thyroid problems can also lead to vertigo. Your symptoms really are not consistent with Alzheimer's disease, parkinson's disease, or ALS, so you can rest these fears.
If by dizziness you mean light-headedness, causes could include low blood pressure such as due to dehydration or autonomic dysfunction, cardiac problems, and several other non-neurologic causes. Anemia can cause light-headedness as well.
If you have not been evaluated by an ENT specialist, I recommend you do so if you experience vertigo. however, seeing continued follow-up with your neurologist and exploring the diagnosis of a basilar migraine may be beneficial to you as well.
Thank you for this opportunity to answer your questions, I hope you find the information I have provided useful, good luck.