What are your actual thyroid hormone levels? They should have tested Free T4 and Free T3, which are the thyroid hormones, along with TSH, which is the pituitary hormone that stimulates the thyroid to produce thyroid hormones.
Please post the results of those tests, along with their corresponding reference ranges. That will give us a better idea of your actual status and we can advise from there.
Have you been retested since starting on the levothyroxine? If so, please also, post those test results.