Regarding your question about RA - I have Hashis and was diagnosed with and treated for RA five years ago. It turns out that I have primary Sjogrens instead with features of RA. Almost everyone with primary Sjogrens will have thyroid disease and arthritis.
Apart from thyroid levels and high protein, inflammation levels in my blood - all the B12, folate and ferritin levels have always been fine with me. Vitamin D was deficient for a while but I have corrected this now and can tell which is causing which sensation now too. When my thyroid is undermedicated I feel terrible - sluggish, lose concentration and can only think about my bed all the time. When it's overmedicated I suffer palpitations and have awful sweats.
When my vitamin D levels slump I feel miserable, achy and even clinically depressed. When the Sjogrens is very active my nerves all tingle (pins and needles) and I feel dizzy with vertigo and fatigued in a way that is almost like narcolepsy and my eyes hurt and feel extra tight and dry. The dryness also causes chronic constipation and thrush and trouble swallowing, hoarseness, reflux plus dry cough and nose bleeds from dry nose.
My joint pain is often bilateral and affects the areas you mention. It would be a good idea to get your autoantibodies checked for Rheumatoid Factor and ANA and if these come back raised then the doctor should refer you straight away to a rheumatologist. If not then it doesn't mean you haven't got RA or a connective tissue disease unfortunately - it would just make it less likely and harder to diagnose. Also they should check your ESR/PV and CRP ask well as a full blood count. There are important measures of inflammation/ protein levels in your blood. With RA or connective tissue diseases they are often very elevated. Hope this helps.