Arduino water pump not working and beeping I’m new to Arduino and am trying to build a plant watering system without much knowledge on the subject. But my water pump is not working as I expected it to. 

I wanted to keep it simple so I bought a Arduino Motor Shield for my Arduino Uno R3. I’m using a motor rated at 3-9V (motor is shown below), I’ve tried two different DC adaptors plugged into the power supply port on the arduino, 12V 1.5A and 12V 2A, even though the motor is rated at 9V, I’ve read that I need a 12V adapter to power the motor shield. 
http://www.mabuchi-motor.co.jp/cgi-bin/catalog/e_catalog.cgi?CAT_ID=rs_360sh

The first problem is If I run the motor at full speed, analogWrite(3, 255), it sounds like its going to explode, so I’m trying to run it at a lower speed. But If use values anywhere below 170 the motor will not run and will only make a beeping sound. 

Secondly, regardless of the PWM value I run the motor at, the chip gets very hot very quickly. 

My question is, why can’t I run the pump at lower PWM values, and why is it getting so hot?
If I bought a 12V water pump and used the same setup, would I not have any of these problems? 

EDIT:
an update...
it seems to basically work now. i have a feeling it wasn't working great because I was previously using a powerbar

It will run on max power PWM(255) for about a minute, and then stop working, which is okay. It will stop and then the motor shield lights will start blinking. Does anybody have any guesses what is happening? The motorshield chip is a little hot, so overheating is a possibility. Or is there not enough current ?

video
https://www.youtube.com/watch?v=xdxf3f_Svqs

void setup() {

//  //Setup Channel A
  pinMode(12, OUTPUT); //Initiates Motor Channel A pin
  pinMode(9, OUTPUT); //Initiates Brake Channel A pin
}


void loop(){
  //forward @ full speed, A
  digitalWrite(12, HIGH); //Establishes forward direction of Channel A
  digitalWrite(9, LOW);   //Disengage the Brake for Channel A
  analogWrite(3, 170);   //Spins the motor on Channel A at a speed. approx 90 is min

  delay(3000);

  digitalWrite(9, HIGH); //Engage the Brake for Channel A

  delay(1000);

}
Regarding your motor just making high pitched noise (beeping) I would say that you are not supplying enough power to your motor for it to pull in the load and get rotating, you might try to first get it started by a higher power setting (PWM) and then when it's running see how far down you can set it before it stalls (stops). 

I don't belive a 12V pump would work any different.

As to the motor and L298 chip getting hot, this is sort of normal and in some cases would require som way of dissipating this heat. A heatsink might be an option. 

If you were to overheat the L298 it will shut down before being destroyed (it should).