I am doing a project in which I want to use both of the modules, but it looks like they both need RX and TX pins.
So, Is it possible to use the both modules by 1 Arduino? Maybe I could put both of the RX and TX pins in series and then Connect them to the Rx and TX pins of Arduino maybe? Would it be a problem?
Mega has four hardware serial ports, therefore no problem. A Uno and its equivalents has only one. You can fix this by having one of the devices on Software Serial. If you are desperate to do this, use the bluetooth at 9600 on software serial. I mention this because I believe GSM devices are typically at 38400, which can be the kiss of death on Software serial.