Get to a service center right away, don't put it off. Pulsing when braking is a sign that the disc is actually warped, and it affects your brakes' stopping power. A spongy pedal adds to the concern. The risk is that roads don't always let you predict when you'll need emergency braking, and with a warped disc you could lose grip at the worst possible moment.
You can make it to the service center, but be careful: drive slower than usual, in low gears, so you don't overheat the brakes any further. Don't drive on busy highways and try to avoid long downhill stretches. Monitor everything closely on the way - if the pulsing gets worse or the pedal goes out completely, pull over and call a tow truck.
After a wash like that, by the way, a lot of people complain about this - hot discs hitting cold water causes thermal shock. Next time you can ask the car wash not to spray high-pressure water directly at the wheels, or just avoid washing the suspension and wheels right after hard driving when the discs are still hot.