How to read a specific amount of data via serial?

I’m trying to send data via serial from my Arduino nano to my ESP. Its an integer from 1 to 4 digits
so something like 0, 13, 1234, 123, …

Every thing works fine but when the data comes too fast it stopps the output and then it print all the data on the screen.

I use this method to recieve data.

void loop() { // run over and over
        if (Serial.available()) {
                incomingByte = Serial.readString();
                Serial.println(incomingByte);
        }
}