Broken iPhone, Need to Recover My Files?

My iPhone's screen is kaput. I can't use the phone's touchscreen, and furthermore the image is so distorted that I could hardly navigate even if I could use the touchscreen.
I'd just get a new phone and trash this one if I didn't have photos on this phone that I needed to keep that haven't been backed up.
The phone has, for lack of a better term, touched itself to the extent where it's disabled itself because the phone registered inputs taken as login attempts.
My question to you is how I go about recovering my data. Should I just get the screen replaced? Is there some software that will allow me to bypass the "Trust Computer" button and the passcode protection, a software that will just break into my phone?
I'd really appreciate some meaningful help here as I'm pretty much at the end of my wits.

I'm afraid you're out of luck, there's no way, bin it.