Thank you for researching and asking
before you get any guinea pigs, some people don't make that effort.
Hay makes up about 75% of a piggy's diet, there isn't really a substitute. As
@helen105281 mentioned, you might not be allergic to some types of hay.
There are a few things you can do to reduce sneezing etc. from hay allergies (I am also a little allergic to hay and grass) :
1. Choose dust extracted hay, this reduces dust which is usually what makes you sneeze.
2. Wear disposable gloves (and perhaps a mask) when handling hay.
3. Store the hay in the shed or garage so you're not exposed to it all the time.
4. Don't use hay as bedding, just use it in their hay racks so it's contained in one place.
As you live in the USA, I would recommend buying the Second Cutting Timothy Hay from here:
http://store.smallpetselect.com/top-sellers-c8.aspx
A blog I looked at a while ago said you can get free shipping at checkout using this code, but it might be outdated, best to try it out anyway though: T32HAY30
That website also sells pellets (in case you didn't know already, piggies need about an 1/8th of a cup of pellets every day), but they don't look particularly healthy to me so it's probably best to use something like Oxbow pellets instead.