Have you asked your guidance counselor? If your school has sent kids to UVA in the past they might be able to tell you what kind of GPA and scores worked. I know you said you go to a rigorous private school so that might be a positive but w/o having that context and just comparing your GPA to an average OOS public school student it’s not the amazing GPA I would guess is required for admittance for an OOS student.
You can see some data on first year UVA students on the UVA website here: Statistics | The Office of Undergraduate Admission
90% of admitted students reporting school rank are in the top 10%. About 1/3rd of admitted students are OOS. Your SAT looks to be within the 50th percentile range but the bar for acceptance is higher for OOS so I don’t know if being w/in that range is good enough.
I think a lot really depends on the rigor of your high school and if it is a school known to UVA admissions. If your high school has a reputation for producing super prepared student with rigorous coursework then your GPA and you athletics might be enough to get you there but if you went to my kid’s high school I would say slim chances.