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Headache in a asthma patient can be due to headaches caused by stressful coughing and wheezing or due to medication induced headaches. In case the asthma is due to allergic nature, it could also result in congestion and resultant headache.
The cause of the headache in the first case is due to low oxygen levels in the body. The headache is one of the body's warning signs that it needs to move into an area where there is more oxygen.
The most common medications that when used persistently, can result in headaches when the medications are stopped. Eg Aspirin, Tylenol and Ibuprofen. Fast acting bronchodilators , used during asthma also can cause headaches.
Other causes of such headaches which can be conditions like cluster headache, severe migraines, tension headaches.
Some measures like saline mist inhalation steam inhalation and titration of your medications might be the initial steps to be taken. Stopping OTC pain killers (in case you are persistently using them) is also needed.
But ultimately, it is important for you to consult your treating doctor, who can evaluate your situation and provide specific solutions.