Since there is still water coming out, and it is coming from underneath
the dash on the passenger side, I would suspect that the water
condensation drain-off system for the A/C on your car has become
plugged, and that the car washing had little or nothing to do with it.

It could also be that your rain rail has become clogged with debris, or
that you have leaking top or window seals, but I would check the A/C
first, this is assuming that you have a working A/C in your car.

If you look at the passenger side close to where your left leg sits,
(U.S. models), there is a small black rubber tube that runs from a
plastic box and goes to the outside of your car. This tube pulls off
easily. The rubber tube could be blocked, but it is probably the plastic
box that the tube attaches to. You can use a coathanger or similar
object to poke free any debris that is blocking the opening in the
plastic box. Be ready with a container for some water to come out,
possibly with gunk in it. I just did this to a 1991 miata yesterday and
it only takes a few minutes.

HTH,

Pat