IPad and iPhone can sync with each other on Notes — how about adding info on the Mac or PC

Syncing the notes to your computer, then moving the notes to your email notes and letting it sync back to the phone would be the easiest.

Without syncing you could email each note to yourself by clicking the envelope icon at the bottom of each note. Then turn it into a note in your email account, of course this would take a long time but you wouldn't have to sync with your computer.

In Notes.app when you are in the "On this iPhone" section, any notes you create will exist only on the phone (not synced with google or iCloud). The option disappears when all your notes are synced, presumably to encourage you to save to iCloud by default, but the solution is simply to leave one in the "on this iPhone" folder.