I have mild allergies, and my doctor always reminds me that often, what sets off a reaction (like your throat tickle) is the "camel principle" - the one straw that pushed the aggravation factors of normal life over the top to create a reaction, however mild. I use an exhaust fan, bought from Calumet 20 years ago, sized to the room as suggested above. I also run a simple Hepa air cleaner (sized to the room) for an hour or so before I go in, and sometimes leave it on while working, depending on the humidity, etc. My darkroom is in the basement, so what I do in the summer is usually more than the winter, and I just monitor my comfort level. Also, the basement has a dehumidifier running all the time.
When selenium toning - which I do occasionally, saving up all prints for a big run, I run the fan and the air cleaner, plus a small fan which blows across in front of me to move the tray vapors toward the exhaust fan. The darkroom door can be open for this too, and a window if the darkroom has one.