Unfortunately, cages are designed/made by people who wouldn't know a budgie from a canary. The sandpaper covered perch could very well be the problem, the sandpaper will NOT help to keep nail growth down, it just makes the bottom of the feet raw.
Even doweling perches should be roughened up somewhat with a rasp.
If you don't feel confident to trim the nails take it to the SPCA or ask someone who has experience doing this.
It is impossible to say if she make a complete recovery without seeing the bird, and even then it is a guessing game.