Trouble with iOS 9 and getting phone to operate normally again?

I'm ridiculously frustrated from the amount of trouble I've had in the last day with my iPhone. For background, I'm with AT&T and have had an iPhone 5c since about August last year (2014). For the longest time I've stuck with iOS 7 because it was simple, I was already used to it, and I didn't have enough space on my phone to upgrade it immediately anyways. I have a phone with 16 GB I believe.

Anyways, as we all know, iOS 9 came out very recently and I figured since I skipped out on iOS 8, why not give iOS 9 a shot? So I downloaded iOS 9 via my laptop and iTunes and about 10 hours or so later, the software was said to be fully downloaded. So I plugged my iPhone into my laptop and this is where all the problems began. After installing the software, the screen went to the gray "slide to upgrade" page, but every time I would finish choosing the settings, it would randomly reset to a gray with black apple screen and the process would continuously cycle.

I attempted to restore a back-up to no avail, all that iTunes said was that an error had occurred and the back-up would not finish. "iTunes could not restore iPhone because an error occurred." Nothing would work. Last resort was to restore my phone completely, which I did and although it didn't work at first, worked after I kept trying about 4 or 5 times. So the phone resets to factory settings, which I can then restore a back-up with only a bit from my iCloud.

Now I notice my iPhone is running agonizingly slow, and that apps are taking more than twice the usual amount of time to download. It starts to freeze up a little here and there, but I think maybe it'll adjust or something. I don't know. Then, this morning my phone is barely crawling along and freezes. I try to force restart it and it goes black, before starting up with the white apple on black background screen. It shows nothing except that for a while, then a loading bar shows up underneath and moves forward maybe 1 or 2 mm. I'm waiting for it to finish and then the screen shuts off again, before repeating the whole process. This whole time my phone has not finished the force restart, and is stuck on the loading up screen for a while, before shutting off and starting all over again. It did this for about two hours before it died, when I tried to recharge it, it turned on and continued to do the same thing.

I can still no longer restore a back-up to the phone, and it won't let me restore the iPhone at all now. I'm all out of ideas. Nothing works. It won't turn off either. Any help?