God gracious yes...ALL the time. I constantly have to remind myself to try and relax them but this actually feels wrong and often painful to do. Once I've relaxed (particularly my legs muscles) a few minutes later I realise I've tensed them up again.
I went for a consultation with an M.E specialist a while ago. She explained that many people with both conditions have developed this as a coping mechanism over time.
In our natural state, we live mostly in a relaxed state but quickly change to being ready for action. I.e the fight/flight response to danger, by our brains dumping a mix of hormones into our blood as a reaction.
Many people with fibromyalgia and / or M.E have had something in their lives where they feel there is always a reason to be on guard. For me this was after having kids and a hubby who ( for all his merits) found dealing with children very very difficult. I spent most of the time bringing both him and the kids up together. Teaching him as well as them what was normal child behaviour and what was naughty, how to react, how to behave basically. This meant I lived on egg shells for a long time without realising it.
Prior to this, I had been in a wonderfully loving family ( still am) but my parents and sister are all different to me in that mess doesn't bother them. At this point, the clinical realised I'd been living with undiagnosed OCD most of.my life and my coping mechanism was to create order and again this affects the hormones your brain produces.
I.dont know whether this helps but for me it really was an eye opener.

I think part of our problem is we all have tense muscles I find myself constantly stretching one muscle or another because it's so tight it's making something hurt.

YES! Everywhere. It is one of my main issues. I think it is due to the pain and our bodies reaction to it. I also think it is, for me, something my body has done so long that it has to be unlearned by my nerves, but super hard to do. I try to do the mental thing, but yes, as soon as I get distracted, they are back to it. I notice it the most when I lay down to bed. I don't know how to stop it!

Neck, shoulders and jaw!

I do this unconsciously, my partner will be like release your hands, that's when i realize that my hands are in balls