
Paul C. answered 07/11/19
Semi-Pro Photographer with a Degree in Film Production & Analog Skills
I'd love some more info on what specifically you are trying to modify about your phone videos. My top guesses are: too much shakiness and poor exposure/coloring.
So then the next question becomes: how much effort/money are you willing to invest in making cell phone videos look better before you take the dive into something that will capture it better in the first place?
While in-phone video stabilization has come a long way, your best bet is to get something to mount your phone to. There are a range of gimbals designed to work specifically with phones to keep the image steady even when you're not. If that's out of your price range, honestly attaching it to a selfie stick of sorts would still improve the shakiness some. Put it on a stick and hold the stick instead of the phone, and you'll find the shaking decreases noticeably. The gimbals will take it a step further, using counterweights or electronics to actually physically compensate for movements you make.
The next part would be color correcting your video in post. Taking your video from your phone to your computer and altering the color to make it look better. I don't know if you currently use any video editing software, but if you don't and don't have the budget for it, I'd take it into iMovie (if you have a Mac). The color options there are very limited, but it's probably your best bet in getting your highlights under control and getting better skin tones.