Answer and Explanation:
- I show my ticket at the counter and check my luggage. Muestro mi boleto en el mostrador y reviso mi equipaje.
I think that instead of "en el mostrador", it should be "al mostrador" because you're "at" the counter, not "in" the counter.
- I listen to music while I wait for my flight. Escucho música mientras espero mi vuelo.
Here, I believe that you should have "para" between "espero" and "mi vuelo" because you're waiting "for" your flight.
Other than that, it looks good!
Hope this helps!