My asthma worsens whenever I take pain medication. Why?

Nsaids? Some asthmatics have Aspirin and other non steroidal anti-inflammatory drug sensitivities; you may be one of these unfortunates. See your pulmonologist or allergist for assessment - you may be started on high dose Aspirin or placed on strict avoidance regimens depending on your risk profile. In the meanwhile, avoid aspirin, ibuprofen, or similar drugs.
NSAIDs such as... ...Ibuprofen or naproxen, interfere with an anti-inflammatory mechanism in the lungs. Try acetaminophen, it is less likely to have that effect.
Very common. Are you talking about drugs like ibuprofen or aleve or aspirin? These drugs interfere with the production of stabilizing bronchodilators called prostagladins which keep your airways relaxed and open. Presence of these drugs can diminish PG-E2 and increase certain spastic substances called leukotrienes. Medications like Singulair (montelukast) may be more effective in people who have asprin sensitive asthma.