If you really feel you need to write it down you can always put a post-it note on the back of your phone, because you probably won’t lose track of it that way.
I use my “reminders” app on my phone most of the time. I have one for “to do” one for “shopping” etc.
However physically writing some things down does seem to help me, and recently I’ve been writing my todo lists on paper to avoid distractions on my phone, and I’m just using my reminders app for my shopping list (because my phone always goes everywhere with me).
It’s completely up to you, but don’t put pressure on yourself thinking that you have to do it like everyone else, it’s also good just to do what helps you.