Really need more information about the car like, is it front or rear wheel drive? Front or rear engine? Does it screech when in park, or only while driving? Is it louder when you hit the brakes?
Here are 2 guesses that it could be. Bad wheel bearings, or sticking brake calipers. Either of which could lockup the wheel & put your car into a skid. This lockup rarely happens, but it's not a good idea to go on a long trip until you find the problem & fix it.
The other posters have good answers too. I would go with the bad belt, or steering pump first.