Congrats on your first game! I really liked the idea and the pixel graphics work well with the pixel-by-pixel drawing/writing system you have.
Sometimes I found it a bit hard to tell where I was allowed to write (especially on the first screen) - maybe you could add some kind of highlight or dashed outline or something to make that a bit clearer?
Another suggestion could be to make it so that if you move your mouse fast it still makes a continuous line rather than a dotty line - I think there's some methods to do this with Line2D, although maybe you coded it a different way :)
Anyway, cool idea, well done!