2003 Grand Am Automatic will shift normal from 1-2 but will not shift into 3 or 4.

Shift - interlock system problem .
Automatic Transmission Shift Lock Control System
The automatic transmission shift lock control system is a safety device that prevents an inadvertent shift out of PARK when the engine is running. The driver must press the brake pedal before moving the shift lever out of PARK position. The system consists of the following components:
• The automatic transmission shift lock control solenoid
• The automatic transmission park lock solenoid
• The automatic transmission shift lock control switch
• The transmission range switch
With the ignition in the ON position, battery voltage is supplied to the automatic transmission shift lock control switch. The circuit continues through the normally-closed switch to the automatic transmission shift lock control solenoid. The transmission range switch provides a path to ground for the automatic transmission shift lock control solenoid in the PARK position. With the automatic transmission shift lock control solenoid energized the shift lever is mechanically locked in the PARK position. When the driver presses the brake pedal, the contacts in the automatic transmission shift lock control switch open, de-energizing the automatic transmission shift lock control solenoid. This allows the shift lever to move from the PARK position. When the shift lever is out of the PARK position the controlled ground contacts in the transmission range switch open. This prevents the automatic transmission shift lock solenoid from energizing when the vehicle is out of the PARK position.

Most of these transmissions cannot be adjusted for slippage. Try an Amaco transmission shop, most will diagnose, tell you what the problem is, and give you an estimate for free.

Some vehicles with automatic transmissions have enough slop to create this noise normally. If the problem just started or has become increasingly worse, it could be due to worn universal joints. The universal joints couple the drive shaft to the drive axle and the transmission on 2-WD and to the transfer case on 4-WD. Another noise that comes from worn universal joints is a squeeking sound at lower speeds. A vibration could also be noticed with worn universal joints.

replace( shifter interlock motor)

I believe there is a sensor inside the transmission pan that should show a code. Bring it to someone who can read the code

No. This is normal in some cars with an automatic transmission. Your transmission fluid can move enough to disrupt it's flow when the car is turned hard and it will change it's function in shifting.
Follow the protocol outlined in the user manual for checking the fluid level.

the reason it might be shifting so early is because of the gear ratio in the rear end of the truck. it is common in the 2 wheel drive basic model pickup because they were designed to work not travel.

Ensure that the transaxle case temperature is 70° to 90° F (21° to 32° C). With the engine running, shift transmission through all gears. With engine idling in PARK, remove the check plug from the transmission. If transmission has been overfilled, allow fluid to drain out. If no fluid drains out, add fluid through the TRANS FLUID fill cap under the hood on the driver side in 1 pint (0.5 liter) increments until it slightly flows from the check plug. Reinstall the check plug.

You will want to check your transmission governor transducer on your transmission, and if you have to replace that...after you begin to drive it the computer system programs the shifting for you. It takes a couple days to get back to normal shifting. Run diagnostic testing on the transmission first, and see if you get a communications failure.

That is simply the mechanism that keeps your car from shifting unless you have the brake applied. It is louder than most vehicles, but that is one small sacrifice for good quality, cheaper car. The noise is normal.