IPhone 5, wouldnt turn on, now is acting really strange?

I've had my iphone 5 since about september 2013. I bought it still with ios 6 ios 7 wsant yet released. When it was i downloaded it and eveything was fine. For the past 2 months or so my iphone shuts off by its self for no reason. To get it to start back up, i have to hold down the sleep and home button for at leasr 20 seconds. This past weekend it would cut off, and restarting it would NOT WORK. It would not turn on at all. This is also with a battery charge of over 80 %. When this fist happened saturday i paniced of course and called apple. My phone had 26 unclean shutdowns. A woman helped me back up my phone, restore it and add all of my info back. She said i should notice a difference, but it hasn't gotten better. Tonight, my phone cut off and would not cut back on again. I went from charging it to the wal to plugging it in to my computer (itunes did not recognize a phone being plugged in) to trying to turn it on not plugged in at all. I finally left it plugged to the wall for 10 minutes, it didn't turn on. Tried my computer again, the wall again, and after holding down the buttons for 30 seconds it turned on. It is now SUPER laggy, which my phone has never been, and i can't even adjust my brightness. When it locks now the screen turns black but is still lit, and i click the home button to make my lock screen come on.
should i take this in to the apple store? I'm really tired of this happening unexpectedly, and i always freak out when it won't turn on.

Go to settings->general->reset->reset all settings.

Other then resetting all the settings the only other thing I could think of is to restore the phone as new through iTunes using a computer.

If that does not work then is probably the phone itself.

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