Can I keep notes on my phone instead of paper?

It depends on the event's Organized Play Level (OPL).

At low OPL (casual/local tournaments), yes — a phone or other digital device may take the place of written note sheets (Rule 417.2). You'd still need to follow the same note-taking rules: your notes must be empty at the start of each match, and you can't refer to notes from outside the current match.

At standard or higher OPL, electronic devices can't be used during matches (Rule 417.1), so you'd need paper notes. The head judge can also further restrict or permit device usage at their discretion (Rule 417.3).

In short: check with your TO or head judge, but for a casual setting your phone is fine.