I accidentally booted into Internet Recovery when I meant to boot into Recovery Manager, will this erase everything on my Mac?
Performing Internet Recovery does not delete your user data.
That said, it is advisable to have a backup ready before performing any other troubleshooting steps.
Under OS X starting with 10.6 (or 10.7?), in order to have everything on your hard drive deleted, you must open Disk Utility and manually reformat / repartition the drive. If you don't do this, only the OS X operating system will be reinstalled, without removing your user data.
So, to summarize, unless you remember going into Disk Utility or doing anything in there, your personal data should be there – even after a restore.