If the blower motor itself is noisy, it may have some debris stuck in the blower wheel. Sometimes we find mice nests in these wheels that cause the motor to go off balance and create noise. To find out, you just need to remove the motor and see if there is anything inside the wheel. If there is no debris then it will need replacing........however a new motor will not cause the original problem you were describing.
If you have the automatic temperature system, there will be a power module for the blower motor that could cause this.
If you have the manual a/c system then it uses a resistor block and that would not keep the fan running....so I assume you have the automatic system.
Yes, it is located under the dash on the passenger side. It is held in place with just a couple of screws and once you have the replacement part it will be even easier to identify.
Your parts store should be able to supply you with a new one.