Addictive pain meds are those that are opioids or narcotics.

Ibuprofen, diclofenac, and acetaminophen are not considered addictive. If your pain persists, you may feel the need to keep taking a pain reliever. This does not mean it is addictive.

At a high level, there are pain relievers like acetaminophen (it is also considered a fever reducer) and non-steroidal anti-inflammatory drugs (NSAIDs) like ibuprofen, diclofenac, and naproxen. These NSAIDs can reduce pain, fever, and inflammation - see this for more, https://my.clevelandclinic.org/health/treatments/11086-non-steroidal-anti-inflammatory-medicines-nsaids.

Side note: Prednisone is not a pain reliever, strictly speaking. Any pain relief experienced from prednisone comes from reducing the inflammation.