If you usually feel uncomfortable when glaring on the water surface, it is necessary to wear a pair of sunglasses. I recommend you to buy a brown or gray sunglasses which has no unnatural contrast, because it can provide eye protection, without changing the color you view through the sunglasses.
If you want to buy the pair of sunglasses to do the fishing, you could choose the polarized sunglasses which will help you filter the bad lights and get the useful lights come in. Your eyes will at the same time be protected from the uv or other lights that may damage your eyes. You could go to the big eyeglasses store to buy one.
Well, it is really good for you to enjoy fly fishing. So, as a matter of fact, the lights reflections on the surface of the water could of course give rise to some damage to your eyes. So, since you want to better protect your eyes and resist those harmful lights, I personally recommend polarized sunglasses to you, which could greatly resist such lights, you can find a lot of them at Walmart, hope you find this useful.