Hi,
Thanks for asking.
Based on your query, my opinion is as follows.
1. Swollen thyroid nodules with new development of lymph nodes is not good.
2. It does not appear to be Hashimotos thyroidits. 
3. It appears to be more possibly 
papillary carcinoma, which commonly present with secondaries/metastasis in the cervical lymph nodes.
4. FNAC or biopsy of the cervical 
lymphnodes or 
ultrasound guided aspiration of thyroid nodules can help in confirmation of diagnosis.
5. It has excellent prognosis. Treatment needs to be started at the earliest. Meet your doctor for test and treatment. 
6. 
Hypothyroidism might be associated also, looking at other symptoms, and will require 
thyroxine therapy. Also Vit D and B12 supplements essential.
Hope it helps.
Any further queries, happy to help again.