Hypothyroid patient use to have side effects like fatigue, weakness and pain in muscles,
stiffness in muscles, increase body weight due to water retention, and
increased heart rate etc
Here you have explain you have mild back pain which is radiating to the chest. There could be few possible causes for this.
1. It may be because of
muscle weakness and stiffness in back muscle as a side effect of
hypothyroidism or
mechanical back pain too.
2.
Chest pain could be because of increase water retention in body and increase heart rate putting more pressure on heart.
Here for both above cases I suggest to do thyroid test and if its not in control do proper treatment.
Even after that if you have mild back pain I suggest to get examine your back with physio or ortho and take treatment. As well follow postural correction and spinal exercises as per physiotherapist guideline.
For chest pain check if it is increasing walking up hill or while exerting yourself with breathing difficulty. If it is increasing then do ECG and tredmill test and based on result
consult a cardiologist for proper examination and evaluation. As well he will also help for treatment.
I am sure you will be fine if you just follow above steps.
Take care