A 27 ACT score is considered 85th percentile (source). A 3.5 GPA is only considered a not strong GPA here in CC land. Are these types of stats typically going to get a student into a very competitive college? No. Is there a way that these stats might still stand a chance at a highly selective institution? Yes. OP hasn’t given us much info about her high school. But I know of many public high schools where the average ACT score is around a 14. 90+% of scores are below 16. There might only be two or three students in an entire graduating class who break 20, with the best of them around a 26 or 27. Now, if OP attends such a school where most people are scoring a 14 and she’s pulled out a 27, perhaps one of the highest that her high school has produced? That might interest a selective college.
Do I think that it’s in OP’s best interest to go to an uber-competitive university where she will have tons of catching up to do? Probably not. But it really depends on the type of individual she is. Some people thrive when they’re a big underdog and playing that catch up game. Other people find it dispiriting and tend to give up, or feel much lower self-esteem even if they don’t give up. I don’t know which type of person OP is.
Apart from her safeties (excluding Chapel Hill) and Howard, her list if a bunch of reaches for all applicants (i.e. small chance of admittance), much less for someone with her stats. If she attends the type of high school I described above, then they might not be impossible reaches. If she attends an upper-middle class college prep high school, then they probably are impossible reaches.
All that to say, OP should definitely vet the supports available at any universities she applies to, particularly those where her stats are well below the 25th percentile.