I wouldn't even use auto-backup. I use "me backup", I copy any important files to my PC and to a cloud account.
As far as the missing ones, I assume they were in internal storage. To recover them the phone has to be rooted. Then you have to install an app like
DiskDigger (the free version undeletes picture files only.) Rooting and installing an app can (may or may not) overwrite some of the pictures you're trying to get back.
If they were on the SD card, just download
PhotoRec to a PC, burn it to a disk. Put the SD card into a card reader, plug it into the computer and use the disk you burned to boot the computer. Tell it to recover from the card to the hard drive. It'll recover anything that looks like data from a known type of file - pictures, texts, videos, music, stuff you never heard of. It's a free program, but it's easily worth $100 or more. (The companion program, TestDisk [same site], can restore deleted partitions on a drive. Also free.) If you've never made a mistake, you don't need PhotoRec, but if you're human, you should burn a disk as soon as you get your first computer. Then deleting that "never happen again" picture, or the report you spent 2 weeks researching, is just a large waste of time, not a tragedy.