The FNA biopsy is a very easy procedure as you see from the other posts.
With the low TSH (mild hyperthyroidism) you seem to be describing, would do I-123 nuclear thyroid scan first. IF the nodules are not clearly hot (I do mean clearly!) then FNA biopsy is necessary to prove they are not cancer. Some nodules over-produce thyroid hormone and are "hot" on nuclear scan -- these are rarely cancer.
I have had this done and it really does not hurt. Only really felt pressure. Not worth the risk of not having it done. Go for it!
A FNA biopsy takes 30 seconds to do and is no different from having blood drawn for a regular blood test. It hurts a bit afterwards, but a lot less than having a sore throat - more of a scratchy feeling. I was surprised - I think the word biopsy scares us off.