Hello and thank you for using JustAnswer Health.
The only medication with a similar profile to Darvocet (as far as scheduling and addiction) is Tramadol (the generic name), which is also sold under the name Ultram or Ultracet (trade name).
It is made in combination with tylenol (acetaminophen), or without tylenol, similarly to how Darvocet was a combination product, and Darvon was the name for the medication (propoxyphene) without acetaminophen.
Other medications given for pain relief for fibromyalgia that are not strictly analgesics but have some analgesic properties are Gabapentin
(Neurontin), Lyrica (Pregabalin). These drugs work by decreasing the sensitivity of the nerves.
Cymbalta and Effexor (of the SNRI class of antidepressants/anti-anxiety medications) have also been shown in repeated studies to help control the pain of fibromyalgia. The SSRI's antidepressant/anti-anxiety medications are known to assist with pain relief as well.
The medication that your doctor has prescribed for you is interesting, but is a more strictly controlled medication than the Darvocet or Tramadol are. Interestingly, Tramadol which has effect on opiate
receptors, is also known to effect Seretonin, which I have read Nucynta does as well. So these medications should be taken with care when given along side SSRI or other medications effecting the seretonin system, although this does not mean they cannot be taken together - precautions to watch for signs of seretonin syndrome would just need to be monitored or doses adjusted as needed.
There are of course the NSAID's, such as Ibuprofen, naproxyn and others. These medications decrease inflammation as well as decrease pain and can be quite helpful. One must take them with food in the stomach, and these medications may not be useful for those that have gastric reflux or other conditions of increased gastric acidity.