Sorry to hear you're having trouble. Sounds like allergies to me, too. The tree pollen is in full swing, and it is really setting a lot of allergies off. I'm on an antihistamines, inhalers, and even prednosone, and I'm still having severe allergy problems.
I have had postnasal drip my entire life. Sinuses definitely can have an effect on your lungs. The nerves that cause mucous/reactions in your sinuses also trigger lungs. If you have a good family doctor, that would be a good place to start. He/she could diagnose your problem, and try some treatment...then if it seems advisable, you could be referred to an allergist. They're sometimes hard to get into, so you might have to start with your general doc. There are some great nasal sprays...Astelin (antihistamine) and Flonase (anti inflammatory) are two I use, and they do help.
If you do have asthma, it will be important for you to get some treatment. You don't have to worry, but you want to make sure that your lungs stay clear. Anxiety over your problems can cause you to feel short of breath, so be sure to keep a positive outlook. If you start feeling very short of breath, though, you need to get help right away. (I'm not saying you are...it's just that if you're not familiar with asthma, you might not recognize the importance of this treatment. Check out asthma sites online, and you'll get educated.
You probably have seasonal allergies and some mild asthma. I would encourage you to get checked out, though.
Good luck to you!