I worked very, very hard to make my school's plastic picc play decently when I was in my high school musical 20 years ago. LOTS of practice...
When I got the school's OTHER picc the next year, it was sooo much easier. I found out that the plastic picc had a crack in it, leaking air.
From what I have read, school piccolos are NOTORIOUS for having mechanical/pad leak issues-probably more so when the band director is a brass player who hasn't ever played a piccolo!
You would think I would have noticed the big crack when I was first playing, but I was pretty oblivious.
So if there is any way to have an instrument repair tech look at it, do. Otherwise, someone who is good at playing the piccoco may be helpful.
After that-practice, practice, practice!
Three days sounds like an inadequate amount of time to get competent for a solo on an unfamiliar piccolo