Some dogs are hypersensitive to fleas. One bite sends them into a chewing frenzy. Even if he's not that bad, he could be more sensitive than most.
I hate blood suckers, ugh!
Yes, grasses, and other plants, can absolutely cause allergic reactions. I've had dogs with that problems.
The best you can do, since you'll probably never know which plant is the culprit, is to just keep it mowed, which I know that you're already trying to do.
Good luck. At least the Benadryl will give him some relief. Please keep us posted on how he's doing.
Love All Life, Thank You For Posting! :)