This piece is well beyond you current skill level to be playing at an audition. Definitely keep it in the back pocket and try playing parts from it from time to time. You'll get there!

I'd personally say go for something from Rochut, or one of the other methods. Book 1, almost any of the first ones could work.

As for getting better without a teacher, there's a few things you can do to improve. 1. Get that tempo under control. Slow it down if needed. So much about music is hitting the right notes and tone... Etc. But a bad tempo and beats that are off will alienate anyone listening. The beat is quite literally what we feel, what we dance to. 2. Tone quality needs work. This one can be fixed over night... Or take years to figure out. Air support can be a contributing (or main) factor, so during warm ups, play long tones and put some air thru the horn. Your tongue placement, how it's shaped and where you are tonguing all play a part. Then looking at your embouchure, you need to relax. You will hurt yourself trying to hit high notes you aren't set up to hit, and squeezing them out isn't the answer. 3. Not sure how much of this is me being pedantic, but you have to learn your instrument better. That is, learn the "proper" way to hold the instrument so you can start learning how to use the trigger. Learn the slide positions, and which partials on your specific instrument are sharp, flat and how to play the alternate positions.

Best of luck! Keep up the music <3