Australia

Sorry for chasing a side point, but I wanted to mention this group that provides a ton of information on dry eye syndrome beyond the very limited resources that my optometrist showed me.

https://www.notadryeye.org/

As for evaporative coolers:

1. they work well when the ambient humidity is low. If the day turns more humid outdoors, they just make noise and don't help. The drier your heat tends to be the more you'll get out of one.

2. be prepared for any effects of the additional humidity you would be adding to your home. If you're not careful you could cause mold and mildew problems. It's best to use one of these only in the hottest few hours and turn it off well before sunset, leaving time for the place to air out. Or if your area is hot enough for AC overnight, you may want to run a cooler only in cycles, leaving time in between to ensure manageable indoor humidity. If the outside temperature happens to drop quickly enough you can end up with condensation and damp indoors.

I live on the coast in a humid area now, so they wouldn't work.

But when I was growing up I lived outback - it was almost desert there and on hot summer days the temperature approached 60C some years. Just standing in the sun for a minute felt like you were dying on those days. Our primary cooling was reflective insulation on the house (we didn't have any thermal mass insulation, I don't think that would have worked).

Reflective insulation is very cheap. If you're on a budget - simple white paint works well (make sure it's rated to withstand UV). It won't do much for you in winter though... you want thermal mass insulation in winter.

Indoor temperatures were still quite high and we used primitive evaporative cooling to deal with that. Fine mist sprays, wet towel on your head (or wet hair), etc etc. It was extremely effective and comfortable.

If I lived in that climate again, I would combine evaporative cooling with air conditioning. Or just use aircon and add a humidifier. We just had solar power and back in those days it was too expensive to buy a system that could run an air conditioner. These days big solar systems are dirt cheap and air conditioners use less power as well.

PS: Larger split system air conditioners tend to produce a lot more cooling, with lower power consumption, less noise, and they dry out the air less than small box window ones. If you don't like aircon.. maybe you just need better aircon? It's not expensive - in fact might save you money if it reduces your power bill.

Our house has ducted evaporative cooling. It works great on dry hot days but is absolutely useless if there’s any amount of humidity. We’re going to get a split system in our bedroom for hot humid days.

We’re in Melbourne so it works well enough for the few stinking hot days we get.

Could dry eyes be more related to a pollen count severity? If so you might want an air filter, and some antihistamines.