Is hydrocodone a muscle relaxer

No.

Cyclobenzaprine is a skeletal muscle relaxant chemically related to tricyclic antidepressants (TCAs) such as amitriptyline and imipramine.

Under Federal law (American) a narcotic only refers to opioids (Heroin, morphine, hydromorphone, oxycodone, methadone) and cocaine.

Under Canadian law a narcotic only refers to drugs classified as schedule I or schedule II controlled substances (opioids, cocaine, hallucinogens, ketamine, cannabinoids).

Medically speaking only opioids are considered narcotics.

Thus cyclobenzaprine is not a narcotic by legal and medical definitions. Cyclobenzaprine is also not a controlled substance in any respect and it it not an addictive drug nor is it a recreational drug

Cyclobenzaprine is indicated as an adjunct to rest and physical therapy for relief of muscle spasm associated with acute, painful musculoskeletal conditions