Depending on how allergic a cat is to something you could see an allergic reaction within hours or days of exposure.

I used to feed Royal Canin Duck and Peas to my RB cat Dusty. It's a good food.

It takes approx 6-12 weeks to know if a new food is eliminating the allergy. You have to be SURE that the cat gets absolutely NOTHING else during that time, no treats, no people food, no milk, etc. If after 3 months there is no improvement then it's probably time to go looking elsewhere for the cause of the allergies. Cats can have allergies to dust, pollen, and things just like people do.

Testing is expensive but may help narrow down the possibilities and if necessary an injection can be formulated for your cats particular allergies. But the testing is not 100% but when the other main culprits (fleas/food) haven't worked it may be a good option to try.

BTW, it only takes the bite of one flea to cause an allergic reaction in an animal that's highly sensitive to them. Does your vet have you treating your cat with anything to prevent them just in case?

I hope things work out for your kitty. I know how frustrating it is to see them miserable and not know what to do to help them faster.