The brand of hay doesn't really matter, but if you find it too dusty and you may be allergic to timothy do consider having a discussion with your parents. Look for non-timothy hay options that come in bulk and a reasonably priced, offer them as options when talking to your parents.
Just remember brand really doesn't matter much when it comes to hay, the best and cheapest hay will probably come from a local farmer in a small bale, but you would need somewhere to store a whole bale.
Personally I feed oaten hay to my guinea pigs, timothy hay is not an option in my country unless it has been imported as it isn't grown here. I get small rectangle bales from a local fodder store (they store them out back in a shed so you have to ask about them). I then store my hay in an old outside toilet building that is unused, I have it on a table so it is off the ground. Good thing about the old toilet building is it has great air flow and is rain-proof.