how long can it take for symptoms of a food allergy to develop and subside?

hi everyone!

starting this off by saying i have an appointment with my vet tomorrow. i just want to make sure i'm bringing her as much information as possible.

i discovered this morning that my incredibly floofy cat has some pretty large bald patches around her neck. i don't know how long they've been there because she is so fluffy that i keep losing the patches when i go to look for them again, but they're at least the size of a quarter. i've found three so far, there may be more hiding. they are completely smooth, not red or raw or scabby. she has not been scratching herself obsessively at all, so this is random enough that i can't immediately explain it.

she is being treated for fleas, and i have double-checked with a flea comb just to be sure she's clean. she brought home fleas from a vet visit (not my current vet, thankfully) about six years ago so i know what the "i'm itchy" sort of wriggling behavior looks like when it's fleas and i am 99% sure it is not that.

back at the end of december, both she and my other cat went on a hunger strike from the dry food i fed them for years (instinct original real chicken). they had previously rejected the instinct fish flavor so i felt like maybe it was an issue with instinct overall like a formula change or something similar, and looked at other brands. the first new food i tried was orijen guardian and it did not go well. they both liked it, but they had foul-smelling poop and she started projectile vomiting after eating after it had been about 2-3 weeks, so i went back to instinct but a different line and flavor (instinct limited diet turkey). they have both been eating the instinct turkey since the end of january.

is it possible that this is due to a sensitivity to something in the orijen dry food and it took a month for hair loss to develop like that? she's floofy enough to camouflage the bald patches but i absolutely would have noticed a patch of that size by now, so it's something that has either happened very recently or has gradually reached this point where they're noticeable. i am not sure if a month after the switch away from the orijen is too long for hair loss to persist if it's an allergic reaction, but i do not have experience with pets that have food allergies so i don't know what is typical or possible.

i'm also not ruling out the possibility that it's the instinct turkey, but given her severe reaction to the orijen, i'm suspicious. i've never seen anything like this and would love any insight before i take her in tomorrow. thank you!