I really think you should develop this further outside of the jam. You've got a cool idea going here, and I think one of the things holding it back is the out of control theme. Using left CTRL works for the them of the jam but I think you could easily improve your game by moving the switch half button to RMB. If you did that I think that switching between the two halves would feel more natural. Also, having damage switch which half you are controlling make the game more "out of control", it also makes it less fun. I got used to hitting CTRL after taking damage, but that seems like a needless step for the player to take. Aside from things like the lake of music or SFX, those were the things I thought could use the most improving. I really do think you could take this game further and make it something really enjoyable. I think that the best moment I had playing was when I realized I could jump, switch halves, and shoot enemies from the air before they could aim at me. Expanding on things like that could be incredibly fun.
I hope to see you in future jams, Marouan!