The noise they make when preparing to vomit can sound like choking. And sometimes, with a furball ("ball" being inaccurate, it's more like a fur snake!), they can fail to expel all of it on the first try and choke a little while getting it all out. Your best bet is to watch and see what is going on. It's going to be vomiting almost all of the time; cat's can get things like bones stuck in their throats - make sure you're not giving your kitty any cooked bones, that splinter easily and can cause problems in addition to choking.
A couple of years ago I took a mini course on pet emergencies. One of components was choking. If you believe your cat is in serious trouble, ie choking on something, you will have to try to get it out. And yes you will get scratched and/or bitten. Anyway, heres what they taught us. Open the cats mouth by holding the cat's head so that the palm of your hand is over the cats head, with your thumb and index finger behind the canine teeth. (Try doing this a few time before you have any emergency). Tilt the cat's nose upwards. Using your other hand open the cats mouth by placing finger on the lower teeth, pressing the jaw down. Look in mouth and remove object. EXCEPT - do not pull on a piece of string wrapped around a cat's tongue. Get her to vet immediately. If you can't see or remove the object or if your cat is struggling too much to let you see inside, pick the cat up by its hind legs, turn it upside down and shake. Slap it on the back while shaking it. This might help dislodge the object.
If your cat has something thats preventing it from breathing, it will lose consciousness. Continue to try and disloldge the object. Do not be afraid of getting your finger in its throat and trying to get hold of the object. Get your cat to a vet as fast as possible. Do mouth to nose resusitation if cat not breathing. Hope this helps.
Cats will also have troubles at the other end; as when they eat a string or ribbon. You won't know until they start dragging "party favors" out of the litter box.
Cut off the string or ribbon as close to the exit as possible and keep an eye on them. They should clear it, but if they seem to be having diarrhea or stomach distress, the vet should step in.
So keep a lookout for these things if your cat likes them too much, and never leave your sewing unattended. A swallowed needle is much more dangerous.