My 98 eclipse is making a screeching noise in the engine

no engine stated, and this varies by ,, engine.

the belts , if new , screech for only 2 reasons
1: loose (or oil soaked, watch a guy last weak oil it to stop this)sad.
2: or the accessory its driving is seized.

id bet the cogged, timing belt will never screech, its idler might.
did you inspect all parts as you asssembled the engine.
no engine stated, so be hard for the blind to answer with savvy,
accurate answers, no?

ACCESSORY belts are tension'ed, 3 ways. (3 classes of systems)
1; manual tension. means you sit it to spec.
2: auto tension'ers
3: some look like auto type and are not.... the book for your engine tells all this.

the cam belt as special tension'g steps, did you follow those.
we cant guess what you did wrong.
nor if you even followed all steps.
below is technician loosing the auto tensioner
if the tensioner feels weak or bad, it is.
my guess, (useless) is that the cam belt is ok
but you skipped the accessory belts tension steps.
if it didnt screech before.

The screeching noise is most likely the alternator belt slipping. The higher RPM suggests that alternator may have failed. There is a second belt for the AC. If the alternator belt is self destructing, be aware that it runs the water pump as well, and the engine may overheat. Have the engine checked ASAP.

check your water pump .

if he just turned the cams over by hand then i doubt that he damaged anything as if a valve was open when the piston came to top dead center then it would have stopped moving.the noise isn`t uncommon because the valves springs will make some noise as they are compressed and the rockers will make some noise as they move against the cam lobe and and the valves will make some noise as the valve spring forces the valve shut.if when you aligned the cam marks and they didn`t hit the pistons and stopped you from moving the cams and all timing marks are aligned then you should be okay to start the motor.

Location: left-upper area of block, front

To replace water pump:
1) remove timing belt
2) remove thermostat housing and water pump inlet pipe
3) remove alternator bracket
4) remove water pump and O ring

Pump bushings could be going out if the technician is not properly setting belt tension.

Vibration could be either severe engine miss or, most likely, you should check all engine and transmission mounts for broken rubber.

The guy was correct. Replacing a waterpump has absolutely nothing to do with the timing.

if i remember right those belts are not together cuz your car has two belts on it one that goes from the crank pullel that runs the a/c and alt and then one thats from the crank to the power steering

Probably your fuel pump, have it looked at by a mechanic.

The water pump is driven by the timing belt. If it has been over 100K, it is time for both to be replaced. If it is the drive belts, be sure to use factory belts, and use the proper tension.

The only four rotating items under the hood are
engine
power steering pump
A/C compressor
and smog emission pump.
==== I would check the fluid level on the power steering first. Check for pink fluid leak on the ground,
==== Check the A/C system with the wheel turn to one side and APPLY ALL LOADS.
Example: high beam on,A/C max,radio on and deforster on.
This will give you system a stress test.
All eyes on the pully and locate to part that generate the loud screeching noise.
My bet is on the power steering pump.

Please post more info on the comment window.
I will follow up on it.