Although I am not a doctor either but have had an AN, it sounds like you have a vestibular system problem. However, do keep in mind that many things can cause problems with that system besides an acoustic neuroma (otherwise known as a vestibular schwannoma). The only way to definitively diagnose an AN is by way of an MRI with contrast.
That being said, because the tumor is an overgrowth of the outer covering of the vestibular nerve, most people with ANs experience varying levels of disequilibrium or dizziness. Sometimes these symptoms occur years before the diagnosis and by the time hearing loss (or facial tingling or something else) send a person for an MRI, their brain has already compensated by using the other good vestibular nerve only to maintain balance and no longer have significant balance issues.
Most doctors will rule out inner ear involvement first with the vertigo you are describing, since ANs are relatively rare.
In my case, I have no working vestibular systems on either side. Therefore I experience what you are describing on a daily basis. Grocery stores are not "user friendly" for me so I grab a cart in any store that has one and hang on for the bulk of the time I am shopping. Needless to say Black Friday held no allure for me whatsoever! Looking up and down or side to side too quickly is something I have learned not to do if I am standing and not near something or someone to hang on to.
Just remember these symptoms can also be experienced with other medical conditions, as well.
Let us know what you find out.
Clarice