Honda Accord 2010 Transmission Problems?

Right out of the carwash my car began to show some electrical/transmission problems. After driving for about 10 minutes the D (drive) light begins to blink and the car seems to have a hard time switching gears. It takes longer for it to go from 1st to 2nd and so on, and om top of it, it doesn't go on 4th gear at all. NOTE: Right Out of the Carwash!

So was it an automatic car wash or a do it yourself hand held wand car wash and you hosed down the motor to make it clean?
If you think that water got into your transmission control system circuits use compressed air on all the harness connectors to blow the water out of them. Leave the hood open in the sun for hours to help dry things up.
Then disconnect the battery cables and hold them together for a minute to drain any electrical feedback in the system.
If the shift indicator light still flashes go to the dealer where they have the factory scan tool that can read transmission codes and date to pin point where your problem is. If you go to a transmission shop they will just try and sell you a rebuilt tranny.

So water getting somewhere it shouldn't then seems to be the clue.

I'd guess it had nothing to do with the car wash, unless you powerwashed the engine without covering electrical components.

It's a coincidence. Take it to a shop.