Problems using serial port (TX and RX)

Projects Networking, Protocols, and Devices
3

my code is simple:

void setup(){
  Serial.begin(9600);
}

void loop(){
  int a = Serial.read();
  Serial.println(a);
  delay(500);
}

I believe the serial port is being used by the PC, because I write a data in the serial monitor and I see that it's printed. Maybe the problem is that the port (the only one I have) is dedicated only with the communication with the PC, and ignores the data from the module. How can I test if my module is correct if I need to print my results, and feed with eletricity my arduino using USB (dont know if interferes on the dedication of serial port).

PS: The final project that I am doing does not have an communication with PC

Thanks!