Here's a good way to assess your baseball skills. If a private school is willing to give you a lot of money (scholarship) to play baseball for them you might be a future D1 prospect. If you have to pay them (tuition) to play its less likely so. Keep in mind all you might accomplish is graduating from high school at nineteen.
You also don't have to attend an expensive private school to stay back a year. You could transfer to a Catholic school. Or if you're a stud baseball player how about Saint John's Prep or Xavarian (quality academic Catholic private schools). They're not wickedly expensive compared to BBN.
What is it that you want? Do you want to play for BC or another New England D1? Or do you want to play in the ACC or SEC?
Here's some homework for you ... Research how many New England players left New England per year over the past few years to play for a Power 5. Get some names. Ask your travel coach how you stack up against Ben Bowden (Lynn Classical), Rhett Weismann (BBN), and Tyler Beede (LA) when they were your age.