This is from your sinuses, not the asthma. Get a nasal rinse system and use that in the morning instead of blowing - it will get out of the gunk that dried in there over night without the trauma that blowing causes.
Second, use a humifier at night in your room to increase the humdity, this will help your nose from drying out and irritating the blood vessels causing them to break.
The Content on this Site is presented in a summary fashion, and is intended to be used for educational and entertainment purposes only. It is not intended to be and should not be interpreted as medical advice or a diagnosis of any health or fitness problem, condition or disease; or a recommendation for a specific test, doctor, care provider, procedure, treatment plan, product, or course of action. MedHelp is not a medical or healthcare provider and your use of this Site does not create a doctor / patient relationship. We disclaim all responsibility for the professional qualifications and licensing of, and services provided by, any physician or other health providers posting on or otherwise referred to on this Site and/or any Third Party Site. Never disregard the medical advice of your physician or health professional, or delay in seeking such advice, because of something you read on this Site. We offer this Site AS IS and without any warranties. By using this Site you agree to the following Terms and Conditions. If you think you may have a medical emergency, call your physician or 911 immediately.