Even during basketball season, you can spend one hour a week on hitting. Carve out the time and put in the work.
How much time do you have before tryouts?
What kind of access to practice space do you have?
I'd put the time into your swing rather than your pitching because your coach probably has a plan to get the pitchers ready on a timeline and pitchers don't throw much to start with on day one.
Without seeing either your swing or your throwing motion, I really can't give you specifics. In general, HS players lack balance and proper load and weight shift in their swing. Take a look at these aspects of your swing and work on improving. If you have some video, I'm sure we can help you out.
Never be nervous. Baseball is fun.