Do I have a neutral wire?
It is quite common to have a single white wire being utilized as an always hot feed to a switch. It should, however, be marked with black tape. This is commonly called a switch loop. If you pull out some of these wires, with the breaker off, you'll see that the whit wire from the switch is not bundled in the group of white wires under the red wire nut. Those wires under the red wire nut are your neutrals.