I was using DaVinci Resolve too when I started filming my ice fishing trips, so I get it. The stabilization in there is really pretty good. What you gotta do is first import your video in the Edit tab, then you look for the clip in the timeline and right-click on it. You'll see "Stabilize" right there in the menu that pops up. Sometimes it takes a minute to analyze the video, like a few minutes if it's long, but that's fine you can do something else while you wait.
Once you've started the stabilization, the important thing is to not go overboard with the settings. Like if you crank the slider all the way up it's true it's gonna get super weird with lots of weird effects and some pretty strange distortions. I'd say start around 50-60% stabilization, then you watch the result in preview and you tweak it. Most of the time that's enough to get rid of the little shakes. If your phone really moved all over the place, well you gotta accept it's not magic, there's limits, but for moderate movements it works really well.
Oh and a tip someone gave me years ago: if you can film with better stability from the start that's even better. Like lean on something, use both hands, or even just put your phone in portrait mode instead of landscape that helps quite a bit. But anyway, you already got your video so with DaVinci you should manage fine.