If you don't have much energy and are feeling cold then these are most definitely an indication of slow metabolism and hints at thyroid problems whatever your results say. Fibromyalgia is not a disease (as far as is known) but a syndrome - a collection of characteristic symptoms with unidentfied cause. Don't be fobbed off with this as a diagnosis for your symptoms because it means the medical profession will stop looking!
Many women develop underactive thyroid around the time of menopause, notably through an auto-immune disease caused Hashimoto's thyroiditis.
Recognition and treatment of thyroid problems is shockingly poor on NHS. Any blood test needs to look at thyroid antibodies, and apparently even normal blood tests don't necessarily rule out thryoid problems.
There was a whole article on thyroid UK website about fibromyalgia and thyroid function. A very good friend of mine has fibromyalgia (ie the symptoms/syndrome) but the CAUSE of this is underactive thyroid for which she takes medication. In her case she has a problem converting T4 to T3 so takes a combination, and this keeps her fibro symptoms ( and others) under control. Unfortunately she had to go privately for this which is as I said, shocking in today's advanced times.
I found these links:
https://www.verywellhealth.com/the-thyroid-fibromyalgia-connection-3231681https://thyroiduk.org/about-thyroid-uk/position-statement-fybromyalgia-cfs-me/I couldn't find the article on thyroid uk I read some years ago which was detailed and helpful, comparing the two conditions. The weabite has changed since I was last there!
Another indication of underactive thyroid besides low energy, and feeling tired, and cold is a tendency to weight gain, as well as muscle pain and stiffness especially after exercise. Some of these symptoms are also caused by low oestrogen and/pr testosterone.
Where are you in menopause in terms of what your cycle is doing?
I would urge you to continue to find a cause for your symptoms, write down all that you experience and when by keeping adiary and include your cycle etc - and take it from there, if necessary by getting more blood tests....
There are others more expert in thyroid function than I am and would be able to say whether your symptoms might point to underactive thyroid- I know very little - Wrensong for one - maybe she might read this?
All the best
Hurdity x