It seems almost like she's trying to swallow something, kinda a gagging cough that starts in her throat. Maybe a hairball? Do you have any hairball remedy stuff (or maybe some butter or olive oil would work) to see if that helps? Or some grass she can chew on? Poor Puddles. What a cutie, by the way. Hope whatever it is gets resolved soon.
"To close your eyes will not ease another's pain." ~ Chinese Proverb
“We must not refuse to see with our eyes what they must endure with their bodies.” ~ Gretchen Wyler