I have a Siamese that eats and gags a lot and that licks so much under her armpit it is raw! Today, she had the"runs" but ate a little then hid all day and doesn't want to come out! Gagged as if trying to throw up a furball as usual but nothing comes out! Always gagging! Ricki
There may be more than one problem going on with your kitty. When a cat licks its fur so much that it makes the skin raw, it is almost always an allergic reaction to something and they are licking because they are itchy. Cats are sometimes allergic to something in their food and that allergy can cause vomiting and diarrhea also.
It is possible that she is licking so much and therefore ingesting so much fur that she is having a bigger problem with hairballs than usual. That can cause gagging or vomiting and diarrhea, even if you don't see any hairballs coming up.
Coughing is also often mistaken as gagging. Cats can have asthma and be coughing and assume the same position and make the same sounds as if they were gagging.
You're probably starting to see that there can be various causes for your cat's problems. I've only mentioned 3 and could list several more. The only way to know for sure is for you to have her checked by a veterinarian. She may need allergy testing, a trial of hairball lubricant, bloodwork and/or X-rays before the problems can be diagnosed and treated.
I know all that sounds complicated and expensive, but from your description, it sounds like a much-needed visit to the vet.
Good luck and feel free to write back with more information or progress reports. Best,