Oh, and go see a doctor about the lump in your throat--it could be something else entirely.
Since you are under care of competent allergists, and you are still having problems, I will tell you how to clear your sinuses, at least. If you are under age 45, I have developed an aggressive sinus irrigation that will flush any infection or allergen out of your sinuses, and give you relief for that. It's a little risky, because you have to bend over in a shower to get the saline in all of your sinus cavities. Click on the blue "friggy" on the forum to find my journal with instructions.
If you are older than that, and don't want to risk falling, buy Dr. Grossan's Hydropulse Irrigator--it's like a Waterpik. Some research by the Mayo Clinic, and specifically by a Dr. Jens Ponikau, suggests that many sinus problems like yours, and perhaps many kinds of asthma, are caused by fungal infections of the sinuses and lungs. Dr. Ponikau is searching for an antifungal spray, but in the meantime, i've been through the symptoms you are suffering, including the sleep gasping, but not the asthma, and thorough sinus irrigation removed them all, and cured me.
Good luck