normal glucose levels are typically in the 4.4 - 6.6 range, so your levels are not actually low, nor would they be considered hypoglycemia.
While everyone is different, dry and cottony mouth, with normal blood sugars is likely unrelated.
Have they checked your insulin levels?
Hope you can get to the bottom of this. Sounds befuddling.
Oh my goodness, I've been having same issue lately. Did you or have you quit drinking soda ? Since I quit drinking soda 2.5 months ago, and experience low's a lot, I am always thirsty. Just as you describe, dry, cottony mouth, somedays I can drink several gallons of water. Don't know maybe it's my mouth recovering from soda.
i would think because, it could also have something to do with cotton mouth or your system isn't digesting the healthy fluids you need, so i would drink lots and lots of water :)