Why does cut grass cause allergies?
www.allergicliving.com claims that the cause to such an allergy is not the grass but is actually mold:


  Often patients will have allergy symptoms with fresh cut grass...That's not grass pollen allergy, that may be mold allergy from the molds being stirred up.


The site also mentions that simply having the physical presence of lawn mower "dust" in one's nose may cause symptoms. 

Source: www.allergicliving.com/2010/07/02/outdoor-allergy-grass-allergy-attack