Have you been done the nuclear iodine uptake scan to check for hot and cold nodules?
Was it described the nature of the nodules (simple or complex) in the ultrasound report?
I guess you have Multinodular Goiter, many nodules causing enlarged thyroid gland.
Enlarged thyroid gland can compress vital structures in neck, trachea and esophagus, leading to coughing, difficulty breathing and swallowing problems (something stuck in the throat, sore throat, slight change in voice).
There is often a dominant nodule within a multinodular goiter which can cause concern for cancer (the one that will be checked with biopsy)
These nodules are developed like extra thyroid tissue to substitute and correct the body lack of thyroid hormones (You have right about your symptoms, they are characteristic for hypothyroidism, increased weight and difficulty losing some is sign of hypothyroidism)