One of my cats has a sensitive tummy and eats sheba succulent selection without problems, they come in gravy as well as jelly, different to fresh and fine
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This is Purina one
Gourmet is very similar but not as rich. Have you tried Sheba fine flakes in gravy
Have you got a Pets at Home near you, they give a full refund on some foods if your cat wont eat it, worth asking them if they do it on the above.
You could try sprinkling a little Fortiflora on the food or maybe your cat would like Purina One in gravy or Gourmet in gravy.
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Try putting soil or sand in one of the litter boxes to see if he will use it. Some cats just dont like the feel of litter under their paws but its unusual for them to change their habits at your cat's age.If he uses the soil then you will be able to see if his poop looks healthy.
You could foster a cat from your local shelter then if all is well either consider adopting the cat or go for the cat you choose. I cant imagine a short/ medium or long haired cat would make a difference to your allergies as all shed fur.
It could be an after effect from the anaesthetic or the change of food. Often if their food is changed without a slow transition it can upset their tummies. Just see her the next poop is, it could be soft just this once.
Are you feeding him Chicken as that can cause diarrhea, he may be intolerant to it. Try giving him s boulardii , if he is an adult then one capsule daily, can be split, half in the morning and half in the evening. If he's a kitten then just half a capsule daily. The one I use is Jarrow from...