Welcome to HCM,
Your wife is suffering from Hypothyroidism
and taking 25 Micro gm/day Levothyroxine
and burning may not be related to thyroid problem so it it better to visit Physician and get examined as if any thing is suspected then a EKG to rule out heart problem can be done and if every thing is fine then burning may be due to Acid peptic disorder with reflux which can be easily treated.
To see dose of Thyroxine is correct a TSH
can be done and dose adjustment depend on the result of TSH.
If nothing comes out even it may be little anxiety
, just relax and if your Physician gives some drug take it.
If Hypothyroidism is there this Thyroxine supplementation may have to be given life long.
Please take care