At this point I would hold off using your system until you've recovered the files. The OS hasn't likely destroyed them yet but merely marked them for re-use. So any altered or added file could over-write your important data.
This gets into a bit of a catch22 problem as you need to have access to the recovery app but you don't dare install it on your internal drive. So you'll need to find a friend who has a Mac to either create a bootable external drive or allow you to interconnect it to yours in Target Disk Mode. In either case you'll need to have the recovery app on the other drive. Here's what we use: [https://www.prosofteng.com/data-rescue-recovery-software/|Data Rescue 4] There are others I've found this is one of the better ones.