Its sounds like you may be doing too much?? if so perhaps you need to pace your activity with more rest - especially anything involving the muscles you mention.
Otherwise there are a few natural things that can help a bit, but with FM it can vary from person to person with what works for us.
before I list those though, I learned what I think is probably a very important lesson at the pain clinic - that is that PAIN IS A STRESSOR & stress like over doing things is our biggest enemy -
so where as I was like you in not wanting to pop pain pills like sweets, in fact I wasn't helping myself, because dealing with pain flare ups effectively in the short term, helps stop it becoming chronic IYSWIM - so DO take pain meds when you need them - its important to stop it getting worse.
Also these can help....
Adequate, but not too much sleep - 5HTP can help some people with this
Lavender & Roman Chamomile Aromatherapy Oil can also help with sleep (pillow or bath)
Magnesium supplements &/or Epsom Salts baths - Mag helps your body regulate stress & pain signals, so you cope better - it can also help with migraine.
Clary sage aromatherapy oil rubbed in (in a carrier oil) or in a bath can also help - its a natural Euphoric, so lifts your mood, which raises endorphins - the bodies natural pain killers - its also a natural pain killer.
Black Pepper or Ginger aroma oils can help with muscle aches (in a carrier or bath)
Paingone Pen works for some people on localised pain - £50 aprox from Boots etc - I LOVE mine
Tens machine - again swear by mine - Lloyds pharmacy often have offers on them
Good mattress & pillow - I have memory foam & its made a HUGE difference to how I feel on a morning.
Black Cherry concentrate has been proven to reduce pain, not cheap, but if you can afford it - & it tastes good too - I tried it, found it helped, but not enough to justify the price.
Acupuncture can help - its been proven to be good for FM in trials & I found it good.
Manual Lymphatic Drainage Massage helped me even more
Myofascial release massage also helped - just a shame I can't afford regular treatments on these any more - if you can then try all 3
Sauna helps
Careful graded gentle exersize, especially things like, swimming yoga or pilates - as hard as it sounds - exersize IS very important to us or things can get worse.
Vitamin D - have you been checked for deficiency??? - its common with FM & your GP can give you supplements - or get out & get plenty of sunshine
& most importantly - Laugh lots, learn to laugh at yourself & your "fog" moments, don't panic when your brain shuts down - relax for a few minutes & try again -
& EDUCATE YOURSELF - despite what your GP might say, not EVERYTHING is going to be FM - I'm only learning now with a new GP just how much they can fob you off with, even when they seem good - since my GP went on Maternity leave, I've been diagnosed with a few other conditions that have been previously blamed on FM, but weren't & are treatable - its only taken 8 years