You probably can't choke on water, because it is a liquid and will run right down your throat. But if you have something hard in your throat, you might choke on that! The water might run down the wrong pipe and make you cough. That is basically all the discomfort that water can cause to you.
Water, or any fluid going down "the wrong pipe" goes into your lungs and can cause aspiration pneumonia.
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Um no I don't think you can. That would be physically impossible seeing as how air isn't a solid substance that could block your AIR way.