Same here - don't have any reaction when running, then a coupla minutes after stopping, I start sneezing and get runny eyes! Infact I tweak a hamstring at the end of one run, by bending over to tie a shoe and sneezing whilst at full stretch!
I take a hayfever tab 1st thing in the morning and am fine later on in the day when I run. I now only have to contend with the midges in the park irritating my eyes lol!