Hello, and welcome!
From your description, it sounds like your kitten may have aspirated some water into her lungs. Coughing is her body's way of trying to get rid of the water, but it might not be enough.
It would be advisable to have her seen by a vet as soon as possible, so she can be treated, after a diagnosis is made. They may need to do a chest x-ray to see if there is any fluid in her lungs and then treatment will be given.
I'm glad to hear that she's still eating, but this could turn into a serious problem, if she is not evaluated by a vet today, to know if she aspirated any water into her lungs.
In the future, don't fill the water bowl up to the top, so this can't happen again.
I hope all will be well with your furry girl!
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