What can I do to fix my goiter-like neck? (photos)

I recommend first getting another evaluation with an endocrinologist to evaluate you prior to pursuing cosmetic treatment. Moreover, we do treatment in this area quite frequently. One great option is, a cobra lift, where we combine skin removal, muscle tightening (platysmaplasty), VASER, and J-Plasma all to contour the chin/neck in one treatment. Other options include facetite, ultherapy, and neck lipo. I recommend (upon medical clearance) consulting with a cosmetic dermatologist or plastic surgeon to review both invasive vs. non invasive treatment options. Best, Dr. Emer.

You do indeed look like you have an enlarged thyroid. This needs to be carefully assessed before proceeding to the plastic surgeon's office. In addition to thyroid testing, often an ultrasound will also be performed to assess the thyroid gland. 

it looks like you have a band of adipose tissue in your neck. I had a patient 2 weeks ago. A careful examination by an experienced Asaps board certified plastic surgeon should be able to determine if this is superficial fat amenable to liposuction. Good luck.