Pollen and the molds in organic debris that are kicked up by a mower are your culprits, and there's some irritative effect from any small particles impacting the lining of your nose (just ask those who work with sheet rock). Anyhow, stuff mentioned by prior posts is fine. Keep in mind all over-the- counter antihistamines are sedating except Claritin or its generic equivalents. Indeed, Benadryl and Chlortrimeton are not supposed to be taken if one drives a car (no kidding), although most folks do OK. Of the prescription stuff, Allegra and Zyrtec are great, with Zyrtec making about 10% of folks a bit sleepy. The nasal steroid sprays (Flonase, Nasonex, Nasacort, Rhinocort and so on) work well also, especially over the long run, but are NOT meant to just be taken only when one has a stuffy nose after mowing, as it takes up to 24 hours for any appreciable effect.
So, you've got prevention - as in 1. having someone else mow the lawn (my favorite option), or 2. wearing a high efficiency and occlusive mask. And/or you've got "after the fact" cleaning, which is the salt water (sometimes with baking soda) sprays. The WaterPik device is superb for flushing out a nose, provided you use a diffuser tip (Grossen is just one of many), and not the tooth cleaning tip that comes with the device.
If you just have a stuffy nose after mowing, and maybe snore a bit more that night, it's just inhalant allergy (if pollens involved, called "hayfever"). That's a nuisance. If you wheeze or have trouble breathing (with your mouth open, which takes the nose out of the equation), then it's asthma. That could be a problem, and what I outlined above (and in other posts also) is pretty much a necessity.
Me, I've only got a Fall pollen problem (ragweed, to be specific), so during that season I take a generic (cheap, at SAMS and COSTCO) version of Claritin, and then flush my nose out after the usual 4-6 hours of clogging it up with debris when I brush cut my 7.5 acres. Works OK, and my wife doesnt' kick me about 1am to wake me up because I'm snoring due to a clogged up nose. If you have a bit more of a problem, consider Allegra or Zyrtec, plus the post-cutting nasal flush.