Painkillers do cause certain people to experience allergic reactions, according to eMedicineHealth. Examples of painkiller medications include morphine, codeine and nonsteroidal anti-inflammatory drugs, such as indomethacin and ibuprofen. Approximately 1 percent of the population is allergic to nonsteroidal anti-inflammatory drugs, as reported by About.com.
Symptoms of an allergic reaction to aspirin include hives, runny nose, itchy skin and red eyes, states Mayo Clinic.
Symptoms of anaphylactic shock, a life-threatening allergic reaction, include swollen eyes, lips or tongue; shortness of breath; difficulty swallowing; chest pain; and rapid heart rate. Patients taking nonsteroidal anti-inflammatory medications who experience any of these symptoms should seek emergency medical assistance, according to Cleveland Clinic.