I was diagnosed with severe Sleep Apnea (AHI = 106) May 2014. Been using cpap ever since - have developed a number of ridiculous side effects including pretty much loss of sense of taste and smell, nose stuffed up all the time, lots of gas, loss of energy - went to Ear/Nose/Throat but the medications (Flonase, etc.) really didn’t help because essentially by using the cpap every night, I am driving air up my nose and into my body every night and this then results in the lack of taste, smell, nose stuffed up, etc. bad side effects happening every day (after a night (every night!) of the air up the nose)!!!
The only thing that has helped even a little with these side effects has been by lowering the pressure on the cpap. Please speak to your physician to see if your pressure can be lowered while still achieving the desired level of pressure to deal with your apnea. Perhaps achieving the lowest pressure that is still effective for the Apnea will help with your Asthma-like symptoms. Good Luck.