I strongly recommend swimming for fibromyalgia sufferers. I know exercise can be hard for those with fibromyalgia, but swimming does not put your joints under stress. Swimming also offers resistance, which can strengthen the muscles.
It’s best to pace yourself and increase your swimming time slowly. If you can’t swim that is ok, you could always walk up and down in the shallow end or take water aerobics if you feel confident and strong enough, this consists of standing up in water which is not too deep (well depending on your height that is) and doing aerobic moves. Some place even have different classes for different hardness levels. Aerobics is a great exercise for everyone and unlike normal aerobics doesn’t put stress on the joints therefore there won’t be too much after pain like normal aerobics. Water aerobics is probably best to try after you have strengthen yourself through normal swimming depending on your current strength, unless you feel your strength level are good enough or your currently already swimming.