I would speak up right away before they even take you to the wash sink.

They can pad the edge for you, and be much gentler if you request it.
You can even let them know that you do have a neck strain/injury so they will be even more careful...

I would try Ice as Mark suggests and maybe some Aleve or ibuprofen type if you aren't on other meds that may conflict.
Or alternate heat/ice if that helps.
Might have even been the muscle tension if you began to tense up, then we breath shallowly, so some calming deep breaths on and off should help as well as general relaxation techniques.