I own a 1999 Model ES300 and all of a sudden it started shaking while driving.
First of all, I thought its because a flat tire but tires are pretty good...

Also the Check Engine and VSC/VSC OFF lights are ON in the dashboard...
Does it sounds like a big technical problem?

Often I used to see the Check Engine and VSC/VSC OFF lights appear and go on their own after a few days.

 

You need to go to Autozone and get the codes for the CEL. It could be anything from a bad PCV valve to an 02 sensor. Usually when your car shakes while driving its a balancing issue with the tires but since you got the CEL and the shaking at the same time it seems like it has to do with the engine. I would also look at the throttle body and give it a nice clean-up. How many miles on the car? You could also have a bad batch of winter gas and might wanna try using something like BG44k in your fuel system to clean that out too. Did I cover everything, lol...