Can non cancerous thyroid nodules cause coughing and other symptoms?

[Sashaa11]

I was recently diagnosed with hashimotos but ive had hypothyroid  symptoms for over year now. The past couple of weeks i have noticed swelling in my neck and there has been pain and discomfort. Ive been getting frequent headaches and my glands have been swelling on and off too. I can get pain that radiates up to my right ear and also noticed the mastoid process of the temporal bone on the same side is also swollen. Ive also gotten a cough that wont go away that isnt related to any sort of cold, along with leg and arm cramping and extreme fatigue.
I recently saw an endocrinologist who i thought was terrible. He just kept referring back to old information about me stored on his computer. Every time i tried to tell him how i felt he wouldnt listen and kept saying my tsh levels are "intermediate" eventhough they are 11.8. He said i dont need to go on medication at the moment so im currently not taking anything. I told him how recently before my period i get eye swelling and pain in my right eye but he said it could be an eye infection.  Whilst there he did an examination and said he thinks i have a cyst. Ive also noticed i have two small round lumps on the left side of my neck. Im now awaiting an ultrasound Scan.

Ive been reading online and saw alot of my symptoms are related to thyroid cancer. I was just wondering if you can get a cough from non cancerous cysts? Also what is the process if nodules are found? do they remove them as im having symptoms?