I live in the uk where you can get a finger prick test which checks everything for £99 which is really good value, it checks TSH, FT4, FT3, TT4, Thyroid Peroxidase Antibodies, Thyroglobulin Antibodies, Ferritin, Folate, Vitamin B12 (NOT ACTIVE B12), C Reactive Protein, Vitamin D (25-OH) https://bluehorizonmedicals.co.uk/thyroid-check-plus-eleven.html
It's done by post but I am not sure if you can get this one abroad? I don't know much about goitres personally, but hashimotos is the main cause and that is auto immune. https://en.wikipedia.org/wiki/Goitre
Worldwide, the most common cause for goitre is Iodine deficiency, usually seen in countries that do not use iodized salt. Selenium deficiency is also considered a contributing factor. In countries that use iodized salt, Hashimoto's thyroiditis is the most common cause. Goitre can also result from cyanide poisoning; this is particularly common in tropical countries where people eat the cyanide-rich cassava root as the staple food.
A gentle detox is the only way I know to get rid of symptoms which would include goitres as the thyroid/adrenals are very sensitive to toxins, and in your case Iodine is too aggressive a treatment to detox - I had the same problem and it's took me a year of intensive support techniques and a very careful diet to almost (but not quite) resolve the hashimotos attack I had after taking Iodine for 3 months.