Couple of thoughts/ideas for you… and I am desperately trying to avoid all of the obvious comedy one-liners and puns regarding the theme of your game and the words in your original post… 
So, you say about making it look more sleek/profressional, what do you think that means?
You’ve outlined the story/goal of the player which is great, often the story is what gets missed.
Looking at the level design what strikes me is I don’t see the relevance between the lockers and the story, e.g. why lockers? why are they there?
My thoughts are along the lines of having your scene and obstacles made from things that relate to your story. Another potential option would be to make it more like a top-down kinda maze game, for example, perhaps your squating player is running the corridors of a school, so your corridors, you lead the player through a few different choices of direction before ending up at the “toilets” as the goal.
Hazards/obstacles could be themed around that location(s), so perhaps there’s a janitor that keeps opening/closing the door to the toilets, you have to time that just right to get passed them. Maybe you have a hall monitor who you have to avoid.
You could then have other locations also, perhaps an office workplace, a supermarket and so on. Each could have their own unique obstacles which are in fitting with the theme and / or locations.
Also, with the design of the levels, I would start of fairly simply, like you have above, just easy to navigate, let the player get used to the controls etc. Then later, maybe start to introduce more than one way to get to the goal, but whilst some may be quicker/less fuel consuming, they may have more challenging obstacles.
Whilst it’s not covered in the course, you could consider a fuel mechanic here too, this is going to be fairly grim to explain in words, but I think it may be fitting with the theme of your game. If you could imagine a circular ended bar along the top of the screen which perhaps represents the players bowel, on the left is an area of “gas”, this is the fuel which enables the bottom burps to power your player through the scene. As the fuel runs down, the bar is filled with a long, brown sausage shaped filler which, if it gets to the end indicate that the player has not made it and has “had an accident”.
As I said, fairly grim to put into words but hopefully that paints a picture for you 
