It sounds like you are allergic to something you are breathing in and/or your eyes are being exposed to.
1, HEPA air intake filters can remove pollen and allergens, even cigarette smoke particles from the air blown into the cab & the air pressurizing the cab keeps anything from leaking in around the door seals. The AC cooling helps too.
The JD cab models offer this as may other manufacturer’s cabs as well.
2, Lawn King had a good idea, a mask like a spray painter's rubber one with HEPA cartridges will work as well. These masks do offer some air flow restriction & can get uncomfortable in hot weather. There are masks with powered air flow & even cooling available if you search for them.
See if one of the less expensive white molded dust masks works fro you but some allergy causing particles are so small that they will pass right through them & can only be caught by a HEPA filter. It depends on the nature of what you are allergic to.
3, See your doctor about allergy medicine, something like Claritin might help.
4, A "cool vest" can help relieve that tired feeling, wrap some "blue ice" containers in a towel & wear them in an old vest to cool your body. A firm in FLA had some special packets that didn't get frozen stiff & stayed at 50 degrees so you didn't have to worry about frostbite.
5, When using the open lawn tractor I try to pick my days mowing after a rain, only cutting going upwind & holding my breath when passing back through the dust plume. Maybe it helps but it still makes me feel like I caught the flu.
Good luck.