The best thing I've found is to suck on ice chips all throughout the day. Since I started doing that, I feel so much more hydrated and it doesn't make me sick.
I was told not to drink during or after a meal because it mixed it all up... Maybe wait half hour after eating. As a fellow water chugger I feel your pain. I'm at the very end my new problem is with heartburn and acid.... Drinking water makes it worse, milk and crackers seem to help some but even still I have to drink water... Not a habit I plan on breaking but it's tough when you feel like crap!
Just try sipping water rather than drinking large amounts at once? Some people put fruit in the water for the taste though dont know if that will help with being sick. Maybe try eating first and then having just little bits of water afterwards so youre not putting as much stress on your stomach. :)