i have a similar balance issue....but with a different cause...and my condition is permanent. I lost the hearing and balance mechanisms in my left ear 3-4 years ago due to a viral or auto-immune illness (doctors don't really know) and my balance has never been the same. When I get a comprehensive physical, my doctor does a series of tests that check balance. I'm rock-solid on many and he gets to one test in particular, and with a very slight push, I begin to wobble and lose my balance. It's kind of freaky really.
I'm convinced that it does have an impact on my golf swing but I'm not sure about reading greens.