On Damus, you can broadcast by clicking the 3 little dots on the corner of notes and selecting broadcast. I’ll provide you with an image to demonstrate as well.

Broadcasting does not save duplicates, so you don’t need to worry about rebroadcasting old notes. One cool aspect of broadcasting is you can save notes which aren’t even your own to your private relay. I broadcast and privately back up a few other accounts I follow just as an extra benefit of running a relay.