I am impressed your doc has tested your RT3, so few do. There is a lot of preliminary info out there relating fibro to low thyroid function (and low serotonin levels too). You said your Free T3 is low but not how low. Typical lab ranges are 2.3 to 4.2, The mid-range on this is about 3.25. If you are less than 3.25 then that is your minimum goal to work toward.
Armour certainly isn't a fix-all (despite how much alternative docs push it)and in fact, since it was reformulated and re-released, we have has a LOT of people not be able to get much benefit from it, even people who had done well on it before it went off the market 2 years ago. It is about 3-4 parts T4 to 1 part T3 and if your T3 is low then Cytomel (or its cheaper generic) sounds warranted.
BTW, have you had your anti-TPO and anti-thyroglobulin tested to make sure you don't have an autoimmune thyroid condition. I hope your doc aggressively treats the low T3. Zinc and Selenium and tyrosine are all major thyroid "foods" so you might add some of these and try some tryptophan 1-4 caps when you wake, at mid-morning, mid-afternoon and at bedtime as these will help the fibro symptoms as well.
Have you had your saliva cortisol tested. If you are low cortisol then the thyroid Rxs don't work well and tend to provoke adverse symptoms rather than helping much. Typically I test the adrenals 1st, work on supporting them if needed then direct the person toward a doc who will be aggressive with thyroid Rxs, meaning he or she will increase the prescription dose every 3 weeks if no or little progress is made and treat symptoms, not reference ranges on a piece of paper.
I suggest going online and putting together a checklist of low thyroid symptoms from various sites and checking all that apply (and even rating them from 1-10 in terms of severity). This will help both you and the doc evaluate progress.
Also I suggest doing basal temps (see any site referencing Broda Barnes for instructions).
Good luck and be pushy about getting the care you so obviously need.