I have rarely needed to add anesthetic prior to injecting fillers, and the under eye area is no more sensitive than other areas. The fillers we use already have anesthetic in them which dramatically reduces discomfort already. That said, you certainly can apply a numbing cream 45-60min prior to your appointment (or use an ice pack during the procedure, or take acetaminophen 1 hr prior) and that would reduce the modest discomfort even further. Filling the under eyes is pretty much the most challenging area to treat, so make sure to find a cosmetic skin expert (e.g. dermatologist) who is highly trained and experienced for optimal results and safety, and a natural look.