Is there a way to have both (USB and Touch Screen) working concurrently?
You should post a link to the Elegoo thing you are using. If it were user-friendly, it would have jumpers that let you choose which pins to write serial data and read serial data from. If not-so-user-friendly, the library would let you choose the Serial instance, or SoftwareSerial instance, to communicate between the Elegoo and the Arduino.
Worst case: bend the pins that connect to TX and RX, and solder jumper wires on them and connect them to a different set of TXn and RXn pins.