Yes, you should have your own private personal relay. It will keep a permanent copy of your stuff, plus all your private stuff like drafts and DM's.
For mobile phones, I personally use and recommend Citrine.
https://github.com/greenart7c3/Citrine
For desktop or laptop, Nostr Tray Relay is excellent. You can set your desktop clients like noStrudel to use in in the cache settings screen.
https://github.com/CodyTseng/nostr-relay-tray
Use these in addition to the public relays.