Is there any evidence that acupressure is better than pain pills for controlling fibromyalgia pain?

No: Since the cause of fm is not known, there is no standard treatment. It is generally accepted that it is not a good idea to use "pain pills" (if you are speaking of opioid narcotics) in the treatment of fibromyalgia. There is no "better than", it is whatever works for you, but i would think that any reasonable and safe modality other than pain pills would be "better" for the treatment of fm.

No: Accupressure should be used as adjuvant to pain medications, as well as massage therapy, water aerobics, and healthy lifestyle. They should all be complimentary.