I know I wasn't allergic to ours the first couple years, then whammo I'd go nuts anytime I went in their room (itchy watery eyes, sneezing so bad to the point I'd get sinus infections, and eventually it got to the point I couldn't breathe and would have an asthma attack).
1st thing I learned is that I was allergic to the pine bedding I was using, 2nd thing I learned was that I was allergic to the animals dander, thirdly was the farm fresh hay, and although they couldn't test for volcanic ash (chinchilla dust) after taking a sample to my allergist he felt that being it was similar enough to that of house dust that I was probably allergic to that too.
I couldn't take away my kids beloved pet being an animal lover myself so I experimented and found that carefresh natural (the white, not the brown) did make it easier to breathe...I've just switched to fleece and so far it seems okay too, and that for me at least the allergy meds (certizine, zyrtec, singulair) DO NOT work in regards to going crazy allergy-wise when I'm in their room.
In my experience I believe your best bet would be to try and find someone else in your household to maintain the cages in regards to when it comes to cage cleaning and dusting the chins. I know, easier said than done!
When I can sucker someone else into doing their cage I notice I'm usually fine until about day 3, and that the days there's more urine in the litter are the days that I'm quicker to run into breathing problems...so try to keep the urine in the cage down by placing a "potty" area that can be freshened up daily if need be.
~Good Luck with the allergies, and if you find something that seems to help that I didn't mention PLEASE let me know!
