Try having the AC go out in Houston....so bad.
I had the AC go out in my tiny apartment when I was cooking for Thanksgiving dinner (yes, November...but it decided to shoot up to the 80-90s) and my apartment didn't cool down for days it felt like.
I also know how you feel with allergies and doors being open, I have the same problem. I always want to open windows on cool days to run the AC less, but then I get all puffy eyed and can't breathe well.
But yea, I would agree with lots of fans. Well placed fans.
Also, plan lots of outings!
Pet store visits? Friend's/family's houses with working AC? "Go to the bank" [apparently that was a legit thing to do in Korea before AC was a common thing in houses, on super hot days people would go sit at the bank. or something like that. second second hand story from my BF]
Good luck with the heat!