What I've found really helps for a sore throat - no matter what the cause. Is Traditional Medicinal Throat Coat tea. They sell it at the grocery stores, WalMart, Target - not too hard to find. It smells like black licorice and feet, and tastes a lot like licorice. Not the most pleasant thing, but not awful either. A little honey helps with the taste. It works for hot or iced. Maybe try brewing up a big batch and keeping it iced and sip that during your workout instead of water.
Also, what kind of environment are you exercising in? Outside and it could be pollen or pollutants bugging you. If you're inside is it pet fluff that your sucking in? In a damp basement - mold spores? By the laundry room - lint fluff from the dryer? Or is it just really dry where you're at. Perhaps a humidifier? Really humid? - damp basement again. Humidity just stuffs the heck out of my noggin. And really really dry air gives me headaches, the insides of my head feel all shriveled up.
I'm not trying to comment on your housekeeping skills, just tossing out some suggestions.
Nan