During ragweed season I wear a particulate mask (not the cheap ones they sell for pollen, an OSHA certified painting/sanding mask which is a little bit thicker and more expensive) - BUT, they definitely don't flow enough air for heavy exertion. They're fine for light exertion (motorcycling, gardening). You could wear a mask just to get outside for a walk or a slow commute, get some sunshine, and do your real workouts in the gym until the air clears.

For pollen, I'm lucky that when I'm running or cycling, the effort suppresses my immune system so much that my allergy symptoms basically vanish. Respiratory irritation from heavy particulate contamination is another thing.

I'll be interested if someone comes up with a solution though. We've got a trip to NYC coming up, and it only takes me an hour there to get all the symptoms you're having. I'd love to go for a run in Central Park but I don't see how I'll be able to breathe.