[HairOfTheDog]

Most of the sites I’ve looked at said dogs shouldn’t have onion. And some say garlic is good, some say it’s bad.

Why do you think they need it? What’s it’s purpose?

[BunnySlippers]

Flavor. I’ve heard garlic is good but did not know about the onion.

[TASMANIANRED]

Garlic is used as a flea retardant.

Onions are a no-no in dogs...

[Titan Magroyne]

And some say garlic is good, some say it’s bad. Why do you think they need it? What’s it’s purpose?
As mentioned upthread, as a flea retardant. There's something to the urban legend vis a vis vampires. Unfortunately I've observed no difference when it comes to ticks. My labs would happily eat dried chopped garlic sprinkled on their food, but I just buy a garlic supplement and toss it down their throats daily. The other dog is finicky.

For dry, flaky, itchy skin in general, my vet recommended a pour-over supplement with both omega 3 and omega 6 fatty acids. I use one called Vita-Derm, helps out a lot.

I can't help thinking your doggies' allergy problems are caused by something seasonal. At any rate, I hope you figure out what it is and it stops for good.