The question does ask "or should I make my own engine", which is different situation from making a 2D game on top of basic graphics libraries that's not much at all like existing games. Game engines are generally expected to involve an extensive visual game world with many assets and behaviors to manage, and this project doesn't seem to have one.

For 2D GUIs, there are programming techniques like imgui for making a GUI while keeping the program architecture lightweight. Out of the free existing GUI frameworks, Qt is pretty impressive.