I still think think the OP has made a mistake. Swallow is the wrong verb to use if you mean what s/he says, i.e. that water gets in your throat and you start coughing. I stand by what I said above:
As I see it the OP wants to know how we describe what happens when you open your mouth while swimming and find yourself with a mouthful of water which slips down your throat and makes you cough and/or choke. No swallowing or gulping involved in that, you're inhaling water.Ex long-distance swimmer here. Sorry to nitpick, but if you swallow sea water or chlorinated water you are more likely to vomit than choke, (although I have swallowed a fair amount of both in my time and nothing happened to me). You cough and/or choke if you breathe it in, not if you swallow it. That has happened to me on occasion, whilst swimming in the sea: a wave washed over me once when I turned my head to breathe in.
If you mean when water gets into your windpipe, it is called 'inhaling water'. You can specify 'involuntary' if you want, though it should be relatively obvious that nobody would voluntarily inhale water. 'Involuntary' is used in a medical context to stress that it is a reflex reaction of the body to inhale water when drowning (strictly speaking, to seal the airways and try to expel the water through coughing, but this often results in water being inhaled).
After reading more posts, I might also say "some water went down the wrong pipe", or at least that sounds idiomatic if this were happening while drinking an alternative beverage. (Besides swimming-pool, or sea-water. Not sure how to hyphenate there.)