As a biomedical engineering senior at Vanderbilt, I can tell you one thing; BME at Vandy is one of the most competitive programs at Vanderbilt. Middle 50% of ACT is 33-35.
When I was in high school, I talked to counselors and admissions officers about the process, and I believe I have some decent insight. When a top university like the ones you have listed looks at your stats, they’ll see your GPA, but it won’t mean anything to them. A 4.3 at one high school may be 4.7 at another, or a 3.8 at another. They look at how you performed relative to your peers, which in your case, you seem to have done very well.
However, the reason why standardized tests are also used is to determine whether your high school prepared you well enough to meet the basic requirements and rigor of the university. Universities are sympathetic to different circumstances and understand that not all high schools are the same, but the top universities also don’t want you to come and get overwhelmed by the rigor either. They use the ACT/SAT to roughly estimate how you compare to your nationwide peers.
In my opinion, your ACT is simply not enough to meet these requirements at many universities. Your GPA and performance to others at your school is excellent; if you could manage to bring your ACT up to even a 31 or 32, you might have a shot at Vandy and GA Tech. Perhaps you should consider taking the SAT instead (some students perform better on one test or the other).
And I don’t know where you stand on the politics of this (I don’t want to sound racist or support/hate affirmative action), but race does play quite a bit of a role in all of this. If you are from what they consider an “underrepresented minority in engineering,” (AKA, black, hispanic, or even female), your chances may or may not be better. I’m not saying that if you are a black female, your chances are now 99%. But this is obviously out of your control, so focus on that ACT/SAT!