I recently messed up my iPhone and my screen's busted. I can't tap anything, but it'll tap randomly anywhere and everywhere. So I can't type my passcode and I'm trying to get all my photos back through iPhoto but since my phone died and I need to enter my password... I think you get the picture... Anyways, is there any way for me to get my photos back?
It will do it without unlocking, unless you've restarted the phone or entered so many incorrect passwords that the phone has locked out any further attempts.
If you've restarted it or tried too many times, then you're in about the same position as the FBI in the US right now - in short, no, you can't get it to do anything until it's unlocked.
You could try putting another identical phone side by side with it & tapping in the same place on both phones simultaneously, to see if it will accurately recognise the taps; but if that doesn't work [& be careful you don't accidentally lock out the other phone] then the only real solution is to get the screen fixed, or check your iCloud storage - see if they're all already saved online.