I had the same thing happen on my Chevy and it was the power steering pump that went bad. Usually under $200 to replace and not to hard to do your self or a mechanic can do it in 1-2 hours.
Power Steering Belt could be loose or worn. Power steering pump could be low on fluid.
The power steering pump could be on it's way out.
Could be low power steering fluid. Could also be an animal that has made a nest in your engine screaming.
A nightmare could cause a person to wake up screaming.
The arm on the steering box may be installed incorrectly. also some trucks have a adjustable steering rod. The rod that runs from the steering box to the axle. Could meed adjustment.
Why is your dog screaming? If it is in pain, then yes... it could die from whatever is causing it to scream in pain.
The squealing could be that you need to add power steering fluid. Also you should check the belt that operates the power steering pump, if bad replace it. If the power steering pump is full and the belt is ok, then you may need to replace the power steering pump.
It does sound like the pump is on it's way out. When you steer the car is the pump making a noise? If so then your pump is going out. You might want to have you power steering hoses checked out too. One of them could maybe be bad and sucking in air which could be leading to your intermittint problems.
You could miss the vein
If you have plenty of fluid it could be the power steering pump itself going bad or it could be the rack and pinion assembly.
You could get sick around the vocal or throat area
You could either be in too high of gear or your (if manual)clutch might be going out.