Brief Answer:
Synthroid

Detailed Answer:
Yes it is standard practice to keep the TSH in that range for the first 5 years after thyroid cancer. Once it is presumed cured at the 5 year mark based on thorough assessments, then the synthroid dosing can be changed to the way it is given to people without a history of thyroid cancer.

The symptoms of relatively high doses of synthroid are

Feeling hotter than usual or hotter than others
Excessive sweating
Shakiness / jitteriness
Frequent bowel movements
Feeling of heart racing /fast heart rate / palpitations
Weight loss
Increased appetite
Scant flow during menses
Irregular menstrual cycles
Moist skin
Hair loss
Anxiety / nervousness
Irritability
Fatigue/ weakness
Reduced sleep

However, many of these can be non specific ie they can occur in individuals without any thyroid problems, due to other causes too.

So it is best to rely on the blood test results for TSH and Free T4 and discuss with your Endocrinologist which symptoms are potentially due to the synthroid.

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Brief Answer:
Follow up

Detailed Answer:
0.05 is not severely low but it is lower than normal.

Muscle weakness can occur too. It is important to make sure you dont have vitamin D deficiency which can also cause muscle weakness. A simple blood test for this is called 25 hydroxy vitamin D. It does not require fasting

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