Is pain reliever bad for your overall health?

No: Chronic use of pain relievers can be harmful. Taking Ibuprofen daily for months to years can cause kidney disease & stomach bleeding. Long-term, daily use of tylenol (acetaminophen) can affect the liver, especially if you already have mild to moderate liver disease. Morphine & other narcotics can lead to tolerance. Too much of anything generally is not good but if you need chronic pain relief, there are options.

Yes: I suppose this depends on the pain reliever. However it is generally accepted that long term use of near any pain medication can have long term adverse affects on your well being.