Here is my usual statement regarding OOS admissions:
"Admission of OOS students to UNC-CH is very competitive; and UNC-CH admits OOS applicants in numbers that are calculated not to exceed 18% of an entering freshman class. See “Undergraduate Admissions” on Page 2, here: http://www.admissions.unc.edu/files/2013/09/Admissions__Policy.pdf. As a further example of the difficulty for OOS students to be admitted to UNC-CH, the entering Class of 2020, for example, had a 15% acceptance rate for OOS applicants: http://admissions.unc.edu/apply/class-profile-2/.
If you look at the UNC-CH Common Data Set, under Part C7 it states that standardized test scores, application essay(s), letter(s) of recommendation, and the rigor of your high school record are “very important” academic factors considered for freshman admission, whereas GPA and class rank are “important” academic factors considered for freshman admission. Extracurricular activities, talent, and character/personal qualities are considered as “very important” non-academic factors.
Further, Part C9 of the Common Data Set for UNC-CH, gives you the median 50% for both SAT and ACT scores, as well as the percentage of the entering first-year class falling within certain ranges of SAT and ACT scores; and Part C11 gives you the percentage of entering first-year students falling within a range of unweighted GPA on a 4.0 scale.
By way of comparison, our OOS high school usually has 8-10 students who apply, and 1-2 students who are admitted, each year to UNC-CH; and, with the exception of legacy students, our admitted students have ACT scores of 34+ and weighted GPAs of 4.5+. These successful applicants also were involved in extracurricular activities that showed commitment over time (no “drive-by” ECs), and demonstrated leadership in the school as well as their ECs. Other kids in our city who I know were admitted to UNC-CH recently also had similar academic statistics and non-academic characteristics; and all of these kids were “unhooked” in admissions parlance (i.e., not a recruited D-1 athlete, or a URM, first-generation college student, etc.)."
Specifically with regards to you, I agree with @kjake2000 that your GPA is a little low, IF it is a weighted GPA; if it is non-weighted, you may be in better shape but I would want to know what your weighted GPA is. In terms of your SAT score, according to the concordance tables a 1300 on the new SAT is equivalent to a 27 composite ACT; and if you are not a URM, recruited D-1 athlete, legacy student, etc., that is probably a little too low – especially given that UNC considers test scores as “very important” in the admissions decision.
Insofar as your paucity of AP classes goes, I think that the real issue here is how many AP classes your school offers and whether you are taking them. If you only have 2 AP courses on your transcript but your school only offers that many (or just a few more), that’s one thing; but if your school offers 20 AP classes and you take only 2, then I can imagine that the admissions officers might have some serious questions about the rigor of your high school record – which is another “very important” academic factor in UNC admissions. Since you state that your school offers few APs, the fact that you will only have 2 on your record by the time you apply may not be that much of a disadvantage, however; the important thing is that you take the most challenging courses that are available to you.
In addition to boosting your standardized test scores, work hard on your application essays (it appears that you may have some good subject matter available to you) and be sure that you have good letters of recommendation. Look at the UNC common data set, and sit down with your guidance counselor early this Fall to discuss admissions strategies; if your high school has Naviance, there may be some useful information there for you to discuss with your guidance counselor as well.
Just out of curiosity, have you looked as Case Western Reserve University? I know that it offers, among other things, an 8-year program that will allow you to get both an M.D. and a Ph.D., which might appeal to you; although admission into that program is also very competitive.