Choking with a baby or small child is always terrifying. A Dr I worked with once told me that if your baby or child can cough then they can breathe as you can't actually cough unless you are moving some air. It's when they open their mouth and no sound or gag/cough comes out then they are not moving air and are really at risk. Turn them over in your lap and with a flat open hand 2 firm blows on the upper back in an upwards motion will often dislodge an object stuck in their airway.

As for water in their lungs better to be safe than sorry. A trip to the ER to ensure your bub is OK is always worth it. Don't ever feel silly, if you are concerned seek help. You did the right thing.