As you may know, 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, immigrant family, etc.).
If you are a URM (“under-represented minority”), recruited D-1 athlete, first-generation college student, immigrant family, or OOS legacy, you may have a slightly easier path. Otherwise, focus on getting high standardized test scores, boost your GPA to the extent you can, and work to have really good ECs, essays, and LORs.
Having stated all of the above, your new ACT score is in the ballpark but I think that your GPA is a little low for an unhooked OOS applicant (if you are unhooked). If you have good essays and letters of recommendation, that will help; but the lack (to me, at least) of significant leadership positions in your ECs is a potential drawback, however.
If you think that you will have a really good Fall Semester in terms of your grades, you may consider applying RD instead of EA (when the majority of first-year applicants apply), so any boost in your GPA would be considered in the admissions decision process. I would discuss this decision with your guidance counselor, however.