Make sure that your code uses one SerialPort and not two. Then there is no problem reading or writing to this port.
SerialPort serialPort;
InputStream inStream;
OutputStream outStream;
serialPort = (SerialPort) portId.open(...);
serialPort.setFlowControlMode(...);
serialPort.setSerialPortParams(...);
inStream = serialPort.getInputStream ();
outStream = serialPort.getOutputStream ();
PS: SMSLib is an excellent Java library (ported to .NET Framework as well) which allows you to send/receive SMS messages via a compatible GSM modem or GSM phone. SMSLib also supports some bulk SMS operators. It is free and very stable.