I'm a bit confused from your other point, since it's been a while since I watched season 3. They're called champions because they win their division two years in a row, and they lost to said finals to Karasuno. Why say they made the finals when they win 2x in a row, unless they meant something else? Also, didn't they lose both times to the winner of the best team in Japan? And also, wasn't that the other little guy that has white hair, aka the better Hinata?
Sorry, I made it needlessly complicated. Shiratorizawa are considered the top team in Miyagi, the prefecture Karasuno and Seijo are also in, because they seem to always make it pretty far in the qualifiers. We know for sure they made it to the qualifier finals the previous two years with Ushiwaka, but we don't know if they won and actually made it to Nationals those times. I assume they did, but we don't really know IIRC.
The things we know for sure is that they went to the Inter-High Nationals after beating Seijo at the end of Season 1, and went on to lose in the quarter finals at Nationals (off-screen). We don't know who they lost to. After that is the Spring High qualifiers, where they lost to Karasuno in the finals, aka Season 3.
I think you're confusing a couple of characters at the end there. All we know about the white-haired kid, Hoshiumi, is that he was at the Training Camp with Kageyama and he's really good. We don't know anything about his team beyond their name, Kamomedai.
You might be confusing him with Sakusa, the black haired guy with the face mask who was also at the Training Camp with Kageyama. He plays for a team called Itachiyama, who are the current best team in Japan. He's also one of the top 3 aces in all of Japan alongside Ushiwaka.
I hope this helps to clear things up a bit.