I'll throw in my two (or three) cents...
Vestibular therapy won't cure your dizziness, but it certainly should help. The more balance exercises you do, the quicker your brain will adapt to and learn to ignore the aberrant balance signals coming from the degraded balance nerve on your AN side. That is, the more you walk and do other exercises that challenge your balance, the more your brain will learn to rely on your sight and the propioceptors in your feet to determine whether you are properly balanced or not.
It is not unusual for a small tumor to be causing such intense balance problems. Many AN sufferers go through the worst of their balance-related symptoms when the tumor is still in its early stage.
You should be in no rush to get your AN treated, as yours is very tiny. You should take the time to fully investigate all of your options -- watch and wait, radiosurgery (GammaKnife), radiotherapy (CyberKnife or FSR/fractionated stereotactic radiation) and microsurgery (surgical resection). Most importantly for now, watch and wait is probably advised until you know whether or not the darn thing is continuing to grow. The only way to know that is to get a followup MRI -- typically six months after the first MRI -- to see if the AN has gotten any bigger. Some ANs don't grow at all over the course of 20 years, in which case (assuming your symptoms stay stable and don't worsen) you may reasonably decide to forego treatment completely. All forms of treatment involve considerable risk, so you shouldn't rush into getting treated, especially with a very small tumor such as yours.
How long can you wait? ANs grow at an average rate of about 2 mm per year, although some don't grow at all (this is rare) and others grow at a much faster clip (this is not common). If your tumor were to grow at the average rate and assuming your AN is currently located inside your internal auditory canal (your doctor probably would've called it a cerebollopontine angle tumor, or CPA tumor for short, if it were growing wholly outside your internal auditory canal), here are the critical timelines to be aware of:
1. You probably have around seven years before it would begin to press on your brain stem; that would make treatment more urgent, but not unmanageable by any means.
2. You would probably have around twelve years before the tumor would be so large (over 3 cm in size) that radiation would be ruled out as a primary treatment. You would then be "stuck" with only one choice: microsurgery (which might be your preferred treatment nonetheless, but it's good to have other options open to you).
So you can see, you probably have years to make a decision and plenty of time to research your options. A sudden growth spurt in the tumor or an increase in your symptoms, however, might compel you to seek treatment sooner rather than later. But even so, there is no urgent need to rush into treatment.
It's important to realize that no form of treatment is going to fully restore your balance and hearing; more likely, it will only prevent further deterioration. And it's possible that microsurgery or radiation would damage your balance and/or hearing further. So again, you should not rush into a decision immediately, especially before you've weighed all your options thoroughly and have determined whether your AN continues to grow.
So step back and breathe. Then comb this forum for information and emotional support. Do your research. The decision you make will determine your quality of life going forward, so take your time and make sure you keep an open mind to all of your options.
Most of all, know that thousands of people have gone before you and have come out of this okay. You too will be okay.
Best wishes,
TW