Since the main symptom started after thyroid surgery, i think that is a strong clue that it may be thyroid related. That is why I suggested as a first priority that she get her thyroid levels higher, by increasing dosage of T4. If she has any reaction to B12 or iron supplements, just delay until thyroid levels are good.
I wonder if your mother's description of "burning" could be better described as "tingling"? I have run across that as a symptom of a patient who was hypothyroid.
Taking the 100 mcg of T4 in the morning will spike her levels for 2-4 hours. If she has blood drawn during that time the result will be falsely high. So be sure to delay until after the blood draw, in order to better understand her true levels. Yes, taking 50+50+25 is fine.
Looking at your mother's test results, her B12 could be increased with supplements to get her into the upper part of the range. Her Vitamin D is fine. Her ferritin is way too low. It should be at least 100. Ferritin is a storage form of iron, readily available for use. It is a more sensitive test of iron levels than serum iron. I suggest that she needs to take about 120 mg of iron daily. Not sure what iron supplement is available there, but we have several that have iron plus Vitamin C to help with absorption. I also suggest that she take about 1000 mg of Vitamin C to avoid any gastric issue from the iron.
Most importantly her TSH being in range means nothing. It is unimportant when taking thyroid med. As an example TSH frequently becomes suppressed below range when taking thyroid med, even when thyroid levels are well within range. Your mother's FT4 of 1.o4 is only at 45% of its range, and FT3 is only at 42% of its range. Also, I am sure she took her thyroid med in the morning before the blood draw for those tests, which will cause higher results. To get a more representative result, it is best to delay the thyroid med until after the blood draw. This is even recommended by the AACE/ATA Guidelines for Hypothyroidism, even though doctors never tell you to do that.
So I am quite sure your mother is under medicated for her thyroid issue. I suggest that she should get an increase in her dosage to a total of 125 mcg per day, and in 5 weeks, go back for followup tests, making sure to delay her daily dose until after the blood draw. By the way there is no need to split the dose of T4 med. She could take it all in one dose. After the new test results, we can advise further. Also get her started on the B12 and iron supplements daily.
In the future there may be other issues that become clearer and need to be addressed, after she gets her thyroid levels adequate, along with B12 and ferritin. For now please help get these things done for her.
The sensation of burning is not a common symptom; however, since it started after the thyroidectomy, we have to suspect it as being thyroid related. I am sure the doctor is looking at her TSH and FT4 and saying it is not her thyroid; however, patients taking T4 meds often find that they are not adequately converting the T4 to T3. Free T3 largely regulates metabolism throughout the body. It is very important to know the FT3 level as well as FT4. TSH testing has little use after starting on thyroid med, since the med dose spikes FT4 within a couple of hours and also suppresses TSH for most of the day. So a TSH that is even suppressed below range does not mean the patient is hyperthyroid due to a high dosage of thyroid med. Thyroid med dosage should not be based on TSH level. Instead the patient's med dosage should be adjusted as needed to relieve hypothyroid symptoms, without gong so far as to create hyper symptoms. In some cases the patient will also need to add a source of T3 in order to get FT3 to adequate levels.
You can read about this in a paper I co-authored.
https://thyroiduk.org/wp-content/uploads/2022/10/Patients-Guide-Final-V5.pdf
So the most important thing right now is to get her tested for Free T3. I would also suggest testing for Vitamin D, B12 and ferritin. Those are also important for a hypothyroid patient. I also suggest giving the doctor a copy of the link above and asking that she be treated clinically as described n the paper: for symptoms, as well as FT4 and FT3 levels. Also Vitamin D should be at least 50, B12 in the upper part of its range, and ferritin should be at least 100.
Do you think you can get all this done for her?
You mentioned your mother had thyroid surgery. Was her entire thyroid gland removed?
Please post her thyroid related test results and their reference ranges, as shown on the lab report. Even more important than test results are symptoms. Please tell us about any other symptoms she has.