It's maybe the best if the next thing you do is backup your data. If you have access to a Linux shell on the phone, through adb, the recovery or something, you can make a copy of the data partition.
If you have adb access (not too rare for the installed recovery system to support it), turn ADB on, connect the phone to your PC, and download the data partition with the adb pull pathgoeshere
command. Partitions should be under /dev, but details are device specific.
If you don't have ADB but have a shell and you can run the dd command, you can use that to copy the partition to an SD card. Maybe to a USB storage if it supports that, but that's questionable.
In old days there was a single data partition, but also there was a different place where the "internal storage" resided. Maybe there are now even more partitions, but I'm not that familiar with current android.