What a way to ruin your day
!
Did your mechanic say you'd need a new motor?
I presume the car stalled when this happened, if so you should not need a new engine (no cylinder damage) -- just a way to get the water out of the cylinders and oil (assuming it made it past the rings).
A purist might want to pull the head to check but a shade-tree mechanic approach would be to pull the spark plug and use a hose to blow warm dry air into the cylinders. If you do this for a day or so and change the oil, I bet you'd be all set.
Now if you
can get the car wash to pay for a new engine then of course that is the way to go... but I expect you're going to find some argument from them on that!
Good luck!