Hi, and welcome to the forum! I'm sorry you have had such a thing happen, and we all know what a stop it puts to your quality of life. There are many people here who have had such a "single demyelinating event" and are waiting for the next step.
It is quite common to be treated with a 3 to 5 day coure of IV steroids after suffering such an event. From the nature of your symptoms, I agree that it appears to have been an episode of demyelination. But, I differ a little in the interpretation that was apparently given to you by your doctors. I do not think that MS should have been put aside so quickly.
85% of MS is of the Relapsing-Remitting type. This means that the person has attacks of symptoms (which can be one or a combination of many dozens of symptoms). The attacks are separated by periods of time from a month to years. Attacks may cause symptoms that linger for a long time or that are permanent.
Far and away the most common cause of a demyelinating event is MS. So, the odds are that what you suffered was the first attack of MS. The symptoms of double vision and one-sided numbness are extremely common with MS. With just one attack, they cannot diagnose the disease. However - and this is a big "however" - with symptoms such as yours the neurologist should have given huge consideration to something called a CIS - Clinically Isolated Syndrome. This is a condition exactly like what you have suffered, a first attack and some abnormal physical findings on exam. When the MRI shows even a single lesion the odds that this is MS rise to about 80%. With two or more lesions the odds are greater than 90%.
The fact that your lesion is on the brainstem is further evidence (but not proof) that this is MS. The lesion on the brainstem is quite likely what has caused the double vision, as the nerves that control the movement of the eyes come from the brainstem. You describe a CIS with Brainstem Syndrome, one of the most common kinds.
So, even though you only have a single brain lesion and MS "usually" has many more, you may have just suffered your first MS attack. The reason I explain this is that the wisdom in the field of MS is to consider beginning one of the MS drugs (known as DMDs or Disease Modifying Drugs) when someone has a CIS to slow the further onset of the disease. It doesn't make sense to wait for a second attack (in my mind) because MS is actively damaging the brain and spinal cord even between attacks. It might be a long time before the next attack. You should have all the facts so that you could make an informed decision.
Now, I am only able to say all this given the info you gave us. I may be wrong and this might be a isolated demyelinating event. But, these are not common. They are far less common than MS.
Did your doctors discuss any of this with you? I believe that you should ask your neurologist about this and if he/she isn't interested in discussing it, you should seek a second opinion from an MS Clinic.
Just so you know, I am a physician with MS and I study the literature so that I can give accurate advice.
Your actual question is how long will it take for the double vision to go away. There is no answer. Healing of the myelin sheath around the nerves can happen within a few days to months or years to never. There is no way to predict this. The steroids you received did what they were going to do within the first couple weeks or so of getting them. Anything beyond that is up to your immune system and the repairing abilities of your central nervous system.
So, you have had a "classic CIS with brainstem involvement and a positive MRI." The more aggressive neurologists in the field would be considering beginning a drug to slow this down, because it is (or will be) very likely MS. I would have to go back to the studies to tell you exactly what risk it is of going on to become definite MS and I will do this. I believe that it is about 80%, but I will check for you.
The diagnosis of MS depends on having 2 or more attacks of symptoms suggestive of demyelination and the finding of 2 or more separate areas on exam that show a neurologic deficit. You have had only a single attack, but I suspect that you already have the two different abnormalities on neuro exam - one for the double vision and another that shows decrease sensation in some part of the left side of your body. We have an article that describes in detail the diagnosis of MS. If you wish to wade through it. Here is the link.
http://www.medhelp.org/health_pages/Multiple%20Sclerosis/Diagnosing-MS---The-McDonald-Criteria-revised-2005/show/370?cid=36
I hope you stay around for more support and for people to share their experiences. Also, people who have had a CIS may stop by and give their info. They may also tell you that my information is usually good and I rarely led people astray.
Welcome again.
Quix