I already have a Pokemon Black saved game, but I started another one without thinking if I would leave and delete my past save.
Can I still save the one I started recently or what?
Pokemon has only ever allowed one save file to exist for one game at one time. In Pokemon Black & White (5th Gen), if you start a new game while another game save exists, you will be unable to save your new game.
This is to prevent accidental save-overs of your main game, while still allowing a 'guest' (friend/sibling etc) to have a go of your Pokemon game.
If you want to completely start a new game, you must first erase the old save by pushing and holding UpSelectB at the Title screen. You will then be prompted to erase the old Save file.
Quite easy, either you saved and your previous save is gone or you didn't save and your new save is gone.
I fear it is impossible to have multiple saves, as in any Pokémon game.