That's a Euphonium. I play it too, and you sound great on it. I am way younger than you, and I am at the same playing level so I know how hard it is to learn this at first, but that was amazing.
Emily, Sounds like you have a good start but yes, you must go a little slower preferably with a metranone. Loosen your embrasure a little and put more air through the instrument not for volume but for a fuller tone. On you tube go to Steve Mead Master Class. He is a euphonium master and has some exellent information that might be helpfull for you. Buy the way, I'm 82 years old and play in three bands. Trombone in one and euphonium in the other two. The euphonium is by far my favorite instrument.Do yourself a big favor Don't ever stop playing. You can always find a band to play in and bring yourself a lifetime of enjoyment making music and entertaining others. Best of luck to you.
All in all, you have a nice tone! Try rehearsing with a metronome, you're making some of the runs more difficult than they actually are because you're rushing. I remember when I first started playing baritone/euphonium 19 years ago... My instructor had me playing "In the Hall of the Mountain King" and I was rushing so much that she sat right next to me with a glock block and a drum stick pounding out the tempo (my ears are still ringing, lol).
As a Euph lesson teacher, about 10 seconds in my teacher brain is screaming inside of me "SLOOOOOWER!!!". So yeah...slower lol. I think you're playing what you hear in your head from seeing the movie and need to slow it down so that you pay more attention to the precise values of each note length. Articulation needs a firmer "Too" on the repeated fast notes, the second note on those long drop slurs have too much CHOP (make longer) You play very musically and with a lot of fire in your sound :).
