IPhone 5C won't turn on and goes crazy?

Okay so I don't want to spend money to go and seek service on apple, (because I live on a non contract… Spent lots of money!) but if it is a need, then okay, I'll do that.

I don't know but after I took a shower, I checked my phone and then all of a sudden, it appeared a logo instead of my wallpaper wherein it needs to be connected to the iTunes via PC and like I can't yet because I haven't downloaded iTunes and my brother's playing my laptop so I thought I'll just leave it and press the home button and the sleep/wake button together and yeah it worked, nothing happened.

But it goes crazy a few hours later. It suddenly turns off and there's an apple logo and it shuts down. I thought the solution was to press home and sleep/wake button together but it wasn't the normal thing where it takes 20 minutes or so, it was kinda quick and then it was back to normal but it keeps on doing it until the weird thing is whenever it shuts down, the apple logo had a weird discoloration and stuff. I did the press thing again and when I took a selfie, the screen was kinda green and it turns off.

So I did the press thing again, and it gets weirder because there's an apple logo but after that there's a discoloration and turns off and it goes the same way all over again and it usually stops when I do the press thing.

I tried to download iTunes and then it was fine and when I connected it, it turned on but the same process.

Should I spend my money now lol

Added (1). I thought the problem is using the phone while charging… Isn't it make a problem? Or virus and stuff lol AAYYY SHUTS

Yeah, dude get it fixed. Lol.

No don't spend money on it you are stuck on DFU mode shoot me an email and will tell you what to do or even help by connect to your computer via remote control!

here is my email

luiz.hernandez@me.com

Something is wrong on system check or repair it.