Hello
I have gone through your question and understood your concern.
You mention that you have goitre and your thyroid test result are normal.
This condition is called euthyroid goitre.
Almost all euthyroid diffuse goiters are due to a condition called Hashimoto thyroiditis.(Probably this is even your thyroid diagnosis)
Because Hashimoto thyroiditis may also cause
hypothyroidism, plasma TSH should be measured.
Feeling tired and being overweight can be signs of hypothyroidism.For this reason i suggest to repeat the thyroid function tests(TSH,fT3,fT4) and than to consult a local
endocrinologist because you may developed hypothyroidism and may need thyroid
hormone replacement therapy.
About your cough after eating and feel like vomiting,in my opinion these are not related to your goitre but can be attributed to gastric conditions like gastritis or
Gastroesophageal reflux disease.
So,my answer is:No, all these symptoms can not be related to your goitre and i don't think your fatty liver has more to do with how you feel.
The treatement for you goitre depends to your actual function tests.
If your tests are normal,you don't need a treatement ,but if you have developed hypothyroidism,you need
thyroid hormone replacement therapy.
Hope i have answered to all your questions.
If you have other doubts,feel free and ask.
Regards