In order to diagnose problems with Caddillacs from 2000 and most recent. You need an OBDll diagnostic tool. It has 24 pins in a rectangular coupling that fits into the cooresponding female coupling under the dashboard. the ends are no squared off. Rather angled. You attach this diagnostic tool to the one under the dash and with the key i the on position but, the car NOT RUNNING, you write down the OBDll codes. They start with P0. then 3 digits. These cars have so many sensors, you can't diagnose your problem w/o one. The on board computer constantly reads the sensors and makes adjustments to the engine accordingly. Currently I have just the opposite problem with my 2003 Deville. The cold start high speed idle isn't working at all. I must hold my foot on the gas pedal to keep the car running when cold starting. Most times after the engine has warmed, It will idle at 725 RPM. I have many other problems like none working windows and mirrors, when cold they work for a very short while. Once the engine and computer warm up they stop working which has led me to believe my computer has a bad circuit. I must take It to a service center that can diagnose the problem as problem is beyond the scope of my small OBDll diagnostic tool's capability.
How fast if up a steep hill? if your a DIYr then open the hood and check for vacuum hoses broken or disconnected and look at the throttle linkage carefully . if it's not electric throttle make sure it moves freely & the throttle is closed Tell me the results of these inspections or tow it to a shop but i would not drive it as you described.