I don't have fibromyalgia, so I don't really understand the issue. I had chronic pain for a while, when my boots didn't fit, but that has been solved.
If it just causes pain, without tissue damage, that might not directly affect your ability to skate - but you might not enjoy it as much as you otherwise would.
Some web sites say fibromyalgia is accompanied by stiffness. If that means that your muscles are frozen tight, that might interfere with any kind of athletic activity, and might make skating gracefully more difficult - but some web sites say the stiffness can be temporary. Perhaps a warm-up would help?
You might want to talk to your doctor about this. See if he thinks that skating could cause you physical damage, and whether he has any recommendations.
Outdoor skating frequently makes your feet cold, depending on conditions, which might make them more stiff. You may prefer to skate indoors, and to use boots and insoles that keep your feet warm. You may also want to warm up your boots (e.g., with a hair drier) before putting them on. But, again, I don't understand fibromyalgia - try it for your body to see if it helps.
Of course, I'm sure you already know that skates have to be very snugly fit for good skating and to prevent injuries, which based on info at various websites, is likely to cause pain for you. Perhaps the falls won't help either. But if you get skates that are very expertly fit and modified to your feet, and are well padded, there should be no extra-pressure points to create more pain. BTW, if you use very stiff boots, and they fit you very well, they don't need to be quite as tight. For good fit, it helps a lot to find the very best boot fitter you can. Ask around. Some skaters also see a sports podiatrist.http://www.mayoclinic.org/diseases-conditions/fibromyalgia/basics/definition/CON-20019243
While there is no cure for fibromyalgia, a variety of medications can help control symptoms. Exercise, relaxation and stress-reduction measures also may help.
I assume you have already tried such treatments, and already get whatever benefit you can from them. Hopefully, appropriate treatment helps some.
BTW, I don't know about Minnesota, USA, but there are places in my neck of the woods you could do synchronized swimming, even as an adult. There are also places where you can do other exercises in the water, that don't place a lot of pressure on the feet.
You could try searching at Yahoo or Google for
+"synchronized swimming" +Minnesota +adult
+"synchronized swimming" +Minnesota +masters
says it is for "local synchronized swimmers of all ages".
Anyway, does swimming have to be "synchronized" to be fun for you? I presume swimming is a pretty good exercise for someone who needs to stay low impact, and avoid tight shoes or boots, to control pain, at least if you don't take it to the training levels that a competitive swimmer might.