yes! i have pretty severe allergies which has resulted in allergic asthma so i definetly feel free your pain. i've always had bad allergies, but about 2 years ago they got so out of control i couldn't exercise for 6 months...and that's when i decided to get treated. now i'm able to run half marathons with no walk breaks...so with proper treatment it's 100 percent doable (at least in my case). the most important thing is to find an allergist who is familiar with running/exercise so she or he can put you on a proper regimen so you can be able to function normally. i use a few nasal sprays, and a "controller" inhaler twice a day. it is alot of drugs, but it's better than taking the over the counter pills (i'm so sensitive to drugs..they make me so zombish). the controller eliminates the need for an emergency inhaler (although i do have one just in case), and really allows me to exercise to my full ability.
when you're running...it's just really important to warm up and start out slower than usual and gradually build. i'll do a walking warm-up, and then especially for my long runs, it really takes me a mile to get into my groove out on the road. it's too harsh on your lungs to start too fast. and of course listen to your body and walk if you need. also i find that drinking water, maybe more than most, helps me too.
also i would 100 percent think about getting allergy shots since it's really the only treatment that actually works to "cure" (not that is a real cure for allergies) rather than drugs to control the symptoms. but talk to your allergist and see if it's right for you!