There are SO many reasons for allergies, and most of them are caused by airborne particles.
At one time, I too didn't have A/C, and used (still have) a stand alone Air Filter, which circulates and filters the air. Any number of "density" Filters can be used in those things. I put it on a Timer, and used it in my Bedroom at night. Started the time about a half hour before bedtime, and really helped me sleep better. But, I've used it in the Living Room watching TV, and even after a rather smoky meal had been prepared
They're portable so...