I feel the same, except I can drink plain water while I'm eating something else. It might be actually the fault of the disgusting taste (a common symptom) that lingers in my mouth. Water doesn't mask it so I taste it all the way down. *gag*
I've been drinking juice or milk mostly. I make sure I buy juices that have vit C like orange juice or cranberry, since I like to at least -try- to get -some- nutrition out of the empty calories. Usually it's fine if I half & half the juice with water so I get less sugar. (milk is nutritious enough on it's own, especially considering they add vit D to it here)
You could consider squeezing fresh lemon juice into your water; I've heard that is effective for some people. Possibly also one of those liquid flavor things. Also remember you get liquids from foods too, so you could make brothy soups for liquid, although that will inevitably involve having lots of salt. (I suggest homemade stock if you have time or a slow cooker, or find some store stock made from bone broth... decent nutrition there!)