If you know the specs of your IR xmitter/rcvr then share them. Stuff like what's the wave length the LED's operate at. Let's say your LEDS's operate at near IR, you may get away with using another set of IR's that are IR.
Once you figure out the use of two IR's of differing wavelengths, you will now need to tackle the issue of:
You'll need a MCU with multiple cores. That way you can receive, one core, and send, another core, at the same time.
If you choose a ESP32 you'll need to know how to use freeRTOS.
If you do not really need them to run at the same time, you can try using millis() and the doing multiple things at the same time thing; use the search to find it. There you can get time slicing like operations. If you want to take it a bit further you can look up State Machine.