It depends. Some people say it is painful and others say it's not that bad. I think it actually hurt less than my doctor prepared me for, so that was good. I had one FNA and then a Coarse Needle Biopsy (because my FNA was inconclusive). The FNA wasn't that bad for me personally. The Coarse one hurt more, but I think having a numbing shot before would have hurt just as much or more.
You're going to be a little sore afterwards, so ice will help. But the last flu shot I got was sore for much longer. You can discuss with your doctor how deep your nodule is and how much he or she needs to take as to whether a numbing shot is warranted or worth it. Just try to relax.
Anyway, that's my opinion on the subject. Let us know if you have more questions about this stuff. We're here to help.