This game is pretty funky, I like it. Stylized graphics, nice and simple, good music, and decent level design. The way the walls work with crates is great. And the concept isn't new, but it is treated in a fresh way, and I like that too.
Now for some less positive comments. To me, it is far more a platform game than a puzzle game. Levels feel just a little bit linear, and opportunities to cock up are scarce (but level design means opportunities to fix cock ups are always there, which is good). Personally I like being able to totally mess up a puzzle and have to restart.
I got a little annoyed with the gun and the spikes, because for me, part of the charm of a puzzle is simply getting lost in it (rather than avoiding danger). Danger can be fun, spikes are always nice, but I would really like the puzzle element to be played up more.
The controls are irritating. Really this game would benefit a lot from different control options. The obvious being non-relative controls. Rather than left and right being relative to the character, a system akin to north, south, east west, would be really nice (so the W key would always move me northwards i.e. to the top of the screen).
If you don't want to work on a new control system, then letting me jump with the down key or the s button, would be a good second best.
Obviously being a game jam game, there was a limit to what you could do in the time available. But what you've made is pretty sold and something I wouldn't mind seeing more of.