Is there any safe prescription painkillers that are not narcotic/addictive?

Yes. There are several options available that are non narcotic. Options range from aleve, celebrex, (celecoxib) vioxx to toradol. These are nsaids (non-steroidal anti-inflammatory drugs). You should check with your healthcare provider to see which one is most appropriate.
Ultram. Has proven analgesic properties by working on the same receptor as narcotics without the serious side effects.