Hi, and thanks for your question.
The cough is of concern, as it could indicate heartworms, a bronchial or other respiratory condition, a cardiac problem, or something else that does require an in person evaluation and exam by the vet. The coughing could be leading to the throwing up, and it could be hairballs, as you suspect, or some fur from self-grooming is 'tickling' his throat, causing him to cough/gag, and then throw up.
Regurgitation right after eating can be caused by many factors as well, like eating too quickly, taking in air as he eats, food allergies, as you suspected, because you've been changing his food. If his current food contains any corn, soy, gluten, wieat, dairy products, artificial additives (colors/flavors), and/or preservatives, these are common allergens for cats and can cause vomiting and other intestinal upset. Some well recommended brands of cat food that don't contain any allergens are Wellness, Innova, EVO, Felidae, Blue Buffalo and Halo, available at your major pet supply stores, but there are many others, as well. For the moment, you can raise up his food/water dishes to chest level, and if you feel he's eating too quickly, place a clean, unused golf ball in the middle of his dry food bowl, so he has to eat 'around' it. For canned food, serve on a flat plate instead of a bowl and mash it down with a fork, so it's not mounded up in the middle.
It is advisable to have your furry boy seen in person by the vet, as soon as possible, so you can get a definite diagnosis and then, treatment, if necessary.
I hope all will be well with your kitty.
If you have found this answer helpful
, please click 'Accept
' and leave positive feedback
; if you have additional questions, need more information and/or clarification, please click 'Reply