It is possible to be allergic to water but being allergic to water is very rare.
When you are allergic to water you can still drink water but you will usually not be able to drink tap water that comes from city water supplies.
Sometimes the things and chemicals contained in city tap water can trigger the allergic reaction to the water and actually it may not be the water itself that someone is allergic too.
Because the people allergic to water can sometimes be okay drinking well water or other filtered water so it could actually be the chemicals contained in the water that they're really allergic too.
Also people with allergic reactions to water usually break out with skin rashes or hives.