I had a mouse problem in my apartment a couple of years ago, and the little !@!! left little "gifts" for me in the darndest of places. I ended up searching for all possible openings into the walls separating the individual units, and I found a bunch: Drain pipes, bathtub faucet, and the wiring to the baseboard heaters. Bought an aerosol can of expanding foam (varieties specifically designed to block rodents are available, which should tell you something) and I sealed every opening that I could find, including behind the dishwasher. Well! Not only did that stop all rodent visits, but also maybe 90% of spiders, silverfish and other tiny critters. And I no longer smell cooking from other units like I used to.
Suppose that had the mice had more time to establish themselves, I might have donned a pair or rubber gloves, wet down their mess with a general purpose cleaner like Simple Green, and wiped the slurry away while wet, so as not to create dust, and perhaps not vacuum it either, lest I create an aerosol.
Did your tile cleaner contain chlorine bleach? If so, I wonder if you were inadvertently mixing ammonia + sodium hypochlorite. If so, your reaction may not have been entirely due to an allergy.