iOS 8.4 install failure, 5S wiped(?) after restart!

Tried to install 8.4 over WiFi, but after downloading the update the phone tells me the update can't be installed for no apparent reason.

Did a soft restart, then the apple logo and progress bar showed up! Great, it's updating anyway!

Halfway through the progress bar the phone restarts and shows this:

No buttons were pushed during the "update", nor did I connect the phone to the charger since I was at 85% charge.

Anyone else encountered this?

I don't have access to iTunes for the remainder of the week, what the f*** do I do now?