Welcome to YorkieTalk. If your Yorkie has long facial hair, carefully check her mouth, especially the corners, to make sure she doesn't have a little hair wrapped around into her mouth and going down her throat. Do this in bright light because the hair can be difficult to see.
If it is not hair, and if it is associated only with water drinking, bring her to the vet for an exam if it persists, as you wrote. Could be anything from a little congestion to collapsed trachea. My younger boy did something similar not long ago: coughed and gagged for about 3 days every time he drank water. I think he was snorting some through his nose.
__________________ Kristin, Max and Teddy
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