Not having a thyroid adversely affects conversion of T4 to T3, so it is good that the doctor has changed your med to include some T3. A high FT4 does not adequately compensate for having a low FT3. It is good to split a dose of T3 to take half in the morning and half in the early afternoon.
I do think that the 10 total of Cytomel is not enough to be equivalent to the reduction of 50 mcg of T4, so you will likely need to increase the T3 to get it up to around mid-range, or as needed. to relieve symptoms. The recommended ratio of T4 to T3 would have been more like 17 mcg of T3.
Peripheral neuropathy can sometimes be related to being hypothyroid, causing water retention in tissue and putting pressure on nerves. Fibromyalgia is not a disease, it is a group of symptoms that doctors don't seem to know much about. I would not worry about it until you get your thyroid levels optimized and then give it a bit of time and see how you are feeling.
You mentioned your Vitamin D and ferritin were okay. Please post the actual levels shown on the lab report.
You don't really have to read and absorb all of the first link. Just click on fig 1c and note that symptom relief requires both T4 dose and Free T3 levels to be adequate, in order to relieve symptoms. Something I am sure the doctor will question. All the scientific evidence to support all this is included in the second link. So the doctor should accept it if he takes enough time to read it.
There is other things that I think will help with your specialist. First click on this link and scroll down to fig 1 and click on 1c. It shows the effect of T4 dosages on the probability of having hypo symptoms. But different people can have different results from the same levels of FT4 and FT3. As shown in the graph, even at 150 mcg of T4, a patient will still have hypo symptoms, unless Free T3 is around midrange or slightly higher.
https://www.hindawi.com/journals/jtr/2018/3239197/
Also I recommend reading my paper in this link.
https://thyroiduk.org/further-reading/managing-the-total-thyroid-process/
You should also give a copy to the specialist to help get what you need.
Did you review these typical symptoms from the link above and decide you have none?
Fatigue
Increased sensitivity to cold
Constipation (need to use laxative or fiber)
Dry skin (need to use skin creme))
Weight gain (difficulty losing weight)
Puffy face
Hoarseness
Muscle weakness
Elevated blood cholesterol level
Muscle aches, tenderness and stiffness
Pain, stiffness or swelling in your joints
Heavier than normal or irregular menstrual periods
Thinning hair
Slowed heart rate
Depression
Impaired memory
Enlarged thyroid gland (goiter)h
With your thyroid levels I would be surprised if you had none of these. You would be better served if your T4 dosage was reduced so that FT4 was about mid-range or slightly below. Along with that you would need to add a source of T3 med and gradually increase until you have no hypo symptoms.Usually that would be around mid-range or slightly above.
I suspect that your heart rate is related to the high FT4, and your neuropathy could be related to inadequate FT3 causing water retention which can press on nerve endings and cause pain. Fibromyalgia is only a group of maladies for which the doctors have no good explanation so they came up with the name fibromyalgia. I think you might see some improvement there if you can get your doctor to adjust your T4 med and add some T3 as suggested. Also you need to test for Vitamin D, B12 and ferritin and supplement as needed to get D to at least 50, B12 in the upper part of its range, and ferritin should be at least 100. All three are very important for a hypothyroid patient.
Do you think you can get your doctor to do all this?
Your FT4 is at top of range, yet your FT3 is below range, which indicates the possibility of poor conversion of T4 to T3. But you haven't told us if you were diagnosed as hypothyroid and taking thyroid med. If so what is the med and daily dosage? Even more important than thyroid test results are symptoms. Please go to this link and then scroll down and tell us which, if any of the symptoms typical of hypothyroidism you have.
https://www.mayoclinic.org/diseases-conditions/hypothyroidism/symptoms-causes/syc-20350284