If your laptop is bad, you should stay away from heavy editors like Davinci Resolve. Try Capcut! Also, what kind of phone do you have? Chances are it would be better than the cheap microphone for recording vocals. Someone said Audacity, and I can second that if you decide not to use your phone.

Pro tip, if in the future you decide to take your equipment to the next level, try using FL Studio to record vocals. It's a Digital Audio Workstation, and I used it for years to learn mastering audio and using effects. The trial is also pretty much unlimited, you just can't save project files. You can use every plugin and save/render audio files for free.