On almost all flights to the US you can bring as much water as you want (or can) as long as you buy or fill after security.
Every once in a while there may be an extra water bottle check at the gate where they search all carry on luggage for bottles and remove them. As far as I can tell there doesn't seem to be any discernable pattern on when this happens or not. I've flown the exact same route just a few weeks apart and one time they searched and another time the didn't.
However, this is exceedingly rare these days and from Dubai, you should be fine. In the rare event that they actually do confiscate your water, you should contact the flight attendants when you board and let them know that you'll need lots of water for medical reasons. They will happily accommodate you.
Tip: bring an empty water bottle and fill it after security. Almost all airports these days allow empty bottles and have fill stations in the secure area.