Serial communication using Arduino UNO at 115.2kbps

Hi there,
I am trying to send some strings to an Arduino UNO at 115.2kbps.
At times, it seems to miss out on certain letters/characters in the middle.
Trying at slower speeds seems to work better, though still had issues at 57.6kbps.
Is speed the problem here, or is there something else?
I have this running with another Software Serial Port which is talking to a display using 9600bps. Could they be clashing? If so I can easily move to an Arduino Mega.

Here is the code I am using:

// Input serial information:
   while (Serial.available() > 0){
    //Serial.println("Reading");
   inByte = Serial.read();
   // only input if a letter, number, are input

   if ((inByte >= 65 && inByte <= 90) || (inByte >=97 && inByte <=122) || (inByte >= 48 &&     inByte <=57) ) {
   command.concat(inByte);

     }
  }// end serial.available
  //Serial.println(command);
       if (inByte == 10 || inByte == 13){
        //Serial.println("Pressed enter");
        inByte = 0;  
        if (command.equalsIgnoreCase("string")){
          genie.WriteStr(1, "Received string"); // sends message to screen. 
                  }

        }
        Serial.print("Sent command: ");
        Serial.println(command); // confirms the message sent
        
                  
        //Serial.println(command);
        command = ""; //start over
     }

I am hoping it is a simple error, and nothing fancy. I am of course initialising this with the write Serial.begin command and changing various speeds to try what it is doing.

I am using a 4D display (uLCD-43PT), and it has its own code but I have omitted that here for the sake of simplicity.

Is speed the problem here, or is there something else?

Yes.

I have omitted the rest of my reply for the sake of simplicity.

Have a look at the examples in Serial Input Basics. They should work at any baud rate.

...R