Wow Jane, that sucks so hard.
Being handcuffed can be traumatic. I hope your wrists are okay.
I think you did the "right" thing by shutting up and accepting it. At least, you did the thing that will bring you the least amount of trouble.
In my own personal "mistaken handcuffs miscarriage of justice" incident, I had to do the same thing. It's wrong that they can just handcuff you like that, and it's a tiny difference between "handcuffed and free to go" and "arrested for resisting arrest" around here at least.
Way to go Jane. Maybe someday our police force will reflect justice...