Noise from car amp when grounded to the body
Sounds like you have some suspect wiring and/or less than brilliant electrical systems in your car. The amplifier is highlighting it as you're boosting the small signals a lot more. It's also probable that it does not have very good EMI protection, compared to the OE head unit which has the advantage of knowing exactly how bad the system is going to be.

User28161 missed a major source of the high-pitched whine which is your vehicle's alternator.

First step would be to look at suppression, these problems are as old as the car radio and are very well documented so I won't go into the detail other than to suggest googling &amp; reading up on it.

If you have access to an oscilloscope you may be able to trace the noise back through the system to find out where it's being introduced.

Using good heavy cables for the wiring, and connecting the negative direct to the battery terminal rather than just grounding to the bodywork (copper is a better conductor than steel, your car's bodywork is not designed to be an electrically efficient path, there are spot welds, paint, possibly corrosion...).