We called our pediatrician and specifically asked them if they do the single dose shots and whether they have thimerosal. Then we booked an apt with them.

My daughter got her flu vaccine through the nose spray instead of the shot this year as she was freaking out about getting the shot.

Flu vaccines in multi-dose vials contain thimerosal to safeguard against contamination of the vial. Most single-dose vials and pre-filled syringes of flu shot and the nasal spray flu vaccine do not contain a preservative because they are intended to be used once.
A list of available flu vaccines and their thimerosal content is available.

https://www.cdc.gov/flu/protect/vaccine/thimero...