Fun concept, felt a bit like a visual novel.
I think you can be quite proud of your first game to be honest.
I didn't encounter any real bugs (did notice that you can chain jumping by smashing into the sides of the steps but I'm calling that a feature) and you even figured things out like parallax layers!
One small thing I'd change, is to also make the controls mouse-only, so that it's really a restriction, not only your them (although I found it quite well thought of ^^)