I am in Ireland where...yeah, two weeks is not the norm. However, when I had a referral to an endocrinologist, he said they could do the FNA immediately. Now, this was private, so might be different. But that was my experience.

And I will say try not to worry too much. Even the worst case scenario is not what you might be imagining with cancer. Generally, it just means an operation to remove your thyroid, then medication for life to replace your thyroid function. And possibly radioiodine treatment, which is annoying but no more than that. It is not painful or likely to make you feel sick or anything. It's just that you have to restrict your movements because you are radioactive.