iPhone 5c won't turn on?! I've tried everything!!

I was in Mexico for the last week, phone was working fine. Halfway through on the flight back, I was just listening to my music and my phone was on airplane mode. All of a sudden, my music shuts off and so does my phone and it was at 50% battery. I tried everything, holding the wake/sleep button, holding the wake/sleep button and the home button at the same time for 10-20 seconds, and putting it away for the rest of the flight until I landed. When I landed, I found a plug and tried to charge my phone for about 2 hours and holding the wake/sleep button and the home button at the same time for 10-20 seconds again while it was "charging", but no luck. I am on the edge of going to the Apple Store to get it replaced, and paying TONS of money for it. I have very little money right now since I just came back from vacation. I need my phone for school the rest of the year which is 2 months. I am very upset about this, and so very frustrated. 😟