Asthma can cause runny nose/itchy eyes. The reason I asked, is that allergies alone don't cause your lungs to hurt. You can have allergy induced asthma, as well as exercise induced asthma. You said a couple of things that raised my suspicions...
I have both, but maybe you should have a pulmonary function test, just to make sure. I rarely wheeze with asthma, just feel chest tightness, unless I am very sick, like with bronchitis. It took me awhile to et tis under control, and it's been years since it's bothered me.