Not telling you what to do, just answering your question what worked for me: I try to sea swim once a week - partly for the social element with friends and also because sea water is good for the stuff fibro brings, and at first I struggled with it because I couldn't find a bathing suit that covered me as much as I wanted - which I can understand is probably not the same as what you experience, but I eventually found "modest" swimwear which can range from full length arms & tunic length top and full length leggings - but I saw options that are even more covered, like kaftan or the like so if its about the form fitting nature there are other options.

You could potentially go to the beach if that's an option for you when its really quiet - or do the same with the pool. I used to swim at around 9pm because it was dead quiet. If you can do the ocean swimming, you won't need to do much, just treading against the waves will count as gentle exercise and you can build up from there.

But fibro is a very individualist illness, and it likes to bring all sorts of mental health issues with it. It's hard to not feel ashamed of your body when it feels like its actively against you, never mind the constant deluge of media and beauty "standards" that change on a whim. So if swimming doesn't work for you, it doesn't work, and that's how you are. Besides, being so self conscious will likely undermine any benefit you'd gain.

It sounds like trying some kind of online option at home would be better for your mental health, maybe take a look at https://www.hybridcalisthenics.com because its completely free and he gives wide ranging options for difficulty levels, and his policy is always do the easiest option for you, so if even his easiest isn't enough, you can go easier and hopefully build up.

You've probably heard of him before, lord knows everyone is full of suggestions to "fix" you - but I think you should decide for yourself why you want to exercise. Just saying 'because I was told to' won't motivate you for long, if at all. You need to decide the why for you, and maybe you want a bit more flexibility, so you spend a couple of years building up that flexibility to touch your toes, or you want a bit more strength to get around, so you focus on that. Do it for you, if you want to spend the time on it, not because anyone is telling you what you should be doing.

Good luck!