Don't stress too much about stats, you're still learning how to play, any gaudy numbers you put up as an amateur won't make one whit of a difference over time
Expect the Pro tier to have a little longer tee boxes and slightly faster greens, those are the only differences.
Your short game probably isn't as bad as you think. You have all starter equipment and starter balls. The improvements in your short game will come when you're ready to upgrade your wedges and ball choice - not because the equipment is all that matters, but because better equipment will give you more types of shots to choose from.
At the Amateur/Pro transition, you should primarily think about hitting fairways and greens, the nuance of the game will naturally follow. The Master tier isn't on the horizon yet, you've still got Tour Pro after Pro, so you've got some time before you have to start worrying about that jump.
There are some course walk-throughs on my profile that I wrote a while back. They might help you navigate the courses and avoid some of the common pitfalls that lead to big numbers.
gl in your new tier and congrats!