I know the ice is convenient (and, I've done it) and some chameleons do well with it. But, not all cope well with the cold water. Almost as easy is to take a plastic container (cup?, cleaned out soda bottle?) and put a pin hole in the bottom....set that on the top of the cage. It will take a few tries to get the size of the hole right, so have a few plastic containers to work with. The warmer water seems to be more generally accepted by chameleons.
As you are experiencing health issues with yours, I would think this small, easy change might be worth making. If you read around, you'll find that even for humans drinking cold drinks (however refreshing) is not considered "good for you".