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.
Your symptoms of a drunken feeling are unusual and could be related to a variety of causes. The one that would of course be most concerning is a TIA, or decreased blood flow to a part of the brain, often called a "mini stroke". This would be best assessed by having the blood vessels to your brain checked (with MRA or ultrasounds), heart rhythm monitoring, having a heart ultrasound, and other testing as determined by your neurologist. If a TIA is suspected, medications to thin the blood as well as other interventions depending on the cause.
Regarding your MRI changes, there are multiple causes for so called plaques in the brain. Most often, these are due to what is called "chronic small vessel disease", literally meaning diseased small vessels that supply blood flow to the brain. This is not an uncommon process in the brain and increases with age. This is not a disease in and of itself but rather is a reflection of unhealthy blood vessels, damaged by years of plaque build-up. This is most often due to a combination of several factors including the following: high blood pressure, diabetes, smoking, and high cholesterol. If these factors are well controlled, the damage to the brain can be stabilized and further damage prevented. It is imperative that if you smoke that you stop smoking, take medication to control your blood pressure, cholesterol, and diabetes, eat a healthy diet, and exercise.
Other causes of plaques in the brain can be migraine. People with migraine often have plaques on their MRI that are of unclear cause or significance. Other causes of plaques on MRI can usually be distinguished based on history and symptoms, such as symptoms of neurologic deficit (for example arm weakness or difficulty walking etc). These can also be distinguished based on the MRI appearance. These include, but are not limited to, as mentioned above multiple sclerosis, other demyelinating disease, and inflammatory processes such as vasculitis. These can be distinguished by your neurologist based on your history and physical examination.
The different causes can be determined to some extent by interpretation of various sequences of the MRI. It sounds like your neurologist does not think the pattern of white spots in your brain are typical of multiple sclerosis. Other investigations are sometimes necessary to distinguish the various causes of white matter lesions. A lumbar puncture is sometimes necessary, in which fluid from around the spine and brain is taken out and analyzed with various tests.
I recommend you establish care with a neurologist for further evaluation.
Thank you for this opportunity to answer your questions, I hope you find the information I have provided useful, good luck.
A related discussion, drunk feeling was started.