Nuts, pulses, beans, pulses, root veg, whole grains and salad leaves are all good sources of the most important mineral in the management of Fibromyalgia, magnesium.
Winter is a good time of year to increase these foods as we like our stews, casseroles and soups (comfort foods, basically). Oily fish eaten 3 times a week might control inflammation and cutting out tea and coffee will lessen the intake of caffeine which can help reduce pain perception.
As a reward for all your hard work, a little dark chocolate occasionally probably won't hurt as it can raise mood and contains lots of helpful magnesium too.
As regards weight loss, the answer depends on the cause. 25% of women have a sluggish thyroid, others don't eat too well and some cannot exercise because of problems like fibromyalgia, joint pain, etc. but do try some gentle activity as the feel-good chemicals can ease the pain of the fibromyalgia.
The most important single dietary step to take when trying to lose weight is easier said than done but it is to cut out sugar. Remember that 'low fat' foods are full of sugar to compensate, that recent research demonstrated that aspartame (the artificial sweetener) actually increases sugar cravings and that the weight gain sugar causes tends to be around the middle, an area that is associated with more inflammation in the body.
Stews, casseroles, some lovely puy lentils with fish are all hearty, comforting foods that help control blood sugars but you can be creative in avoiding the sugar in common canned and packaged foods too. For example, baked beans can be full of sugar but doesn't mixed beans mixed into some pesto sauce sound nicer anyway? I call that 'posh' beans on toast. As a rule, increasing plants in the diet, as you will do by following the dietary guidelines for fibromyalgia, will produce the best and most sustainable benefits.
A lot of people do need an occasional break from the discipline of dietary regimes, if only as a reward, and for that reason a lot of people do find the "5:2" diet idea something they can live with. It does still mean you have to adopt the healthier approach through the week but its at the weekend that the hard work is put in. 5 days eating normally, 2 days eating less, hence the "5:2". The body doesn't go into starvation mode, shutting down the metabolism, and the regime isn't hellish 7 days a week. It's well worth considering as I know of many people who mind this programme something they can adhere to.
Best of luck and picture your goals!!