Although we can’t tell what non-addicting medications you have been prescribed, often pain relievers are either medications like acetameniphen (Tylenol), ibuprofen (Advil), or Aspirin. These are nonsteroidal anti-inflammatory drugs (NSAIDs).
Medications like morphine fall into the opioid or narcotic category, which can be addictive.
NSAIDs act on pain by reducing swelling at the site of the pain so the pain will be relieved. Opioids, on the other hand, interrupt how your brain receives the pain signals. If the medication is working, your brain will not feel the pain signals as they are sent from the injury to the brain.