I'm and ENT doctor...... and so much more
anyway, alkaline dust like playa dust isnt a true "allergy", it is an irritant and certainly some people are more subject to problems than others. You do what you can. A few statements that may help
antihistamines are unlikely to help at all.
steroids are likely to help, but have side effects of course. using topical steroids will likely help but they arent as effective as those taken orally. Here's what I would do
Get flonase and azmacort and use both the whole time, flonase is a nasal steroid and azmacort is a steriod lung puffer. they have basically no side effects if used for a week or so.
get some oral steroid pills to take if you have a flare up and an albuterol inhaler, both are cheap and safe if you just use them should there be a crisis.
probably the most important thing to consider, and my suspicion from your short post, is that it may not be the dust alone, or the dust as much as you think.... other things are different on the playa, not just dust. your diet is different, you are likely drinking on odd schedules and eating on odd schedules. By far the most common cause of losing your voice and having terrible throat problems come on suddently and unexpectedly is laryngopharyngeal reflux. You dont need heartburn or indigestion symptoms and it may be hard to prove if it is a factor or not, but it is easy to treat.
I would get OTC Zegerid antacid, buy the 3 pak of 42 its cheaper. Take two of them (40 mg) about a half hour before you lay down to go to sleep every time without fail regardless of if you are having voice problems or breathing problems or heartburn or indigestion. I bet this advice would help more than anything else, but wanted to adress the dust first since you feel like it is the problem, and you may be right (or partially right as there can be coconspiring issues).