Asthma/Allergic reaction to secondhand smoke in apartment complex.. what can I do?

You can contact your landlord and see if he/she will be willing to fix the area so that no odors can come from the apartment next door. Read your lease and read your state's landlord/tenant responsibilites. The tenant/landlord responsibilities can be found on your state's website. If the landlord won't or doesn't have to fix the area, then use duct tape to seal off the area. It may look ugly, but duct tape never fails.