To track your GPA and see what’s possible, create a spreadsheet (Google Sheets works well) and log all of your classes and grades. Then, to look at hypotheticals, create duplicate tabs and put in the grades you hope to get in current/future classes. It’s easy to calculate real and projected GPA’s from there - sum the columns and divide. You can use this to track your grades as you go along.
If you’re a sophomore now, your 3.48 is only for 9th grade, correct? Because you wouldn’t even have fall semester grades finalized for this year. So yes, it’s mathematically possible to get to a 3.8 by the time you’re doing college applications. Whether it’s possible in real life is a separate question. And as you say, passing up opportunities like your research project, just to protect your GPA, is not going to get you to a single-digit-acceptance-rate college anyway. So seek out challenges, and if your GPA isn’t perfect, then it isn’t - there will be plenty of great places you can go to college, whether NYU ends up on that list or not. As DadTwoGirls says, focus on good habits and depth of understanding, not on grade-grubbing for its own sake.
It’s also worth noting that some colleges don’t even consider freshman grades. Two top business schools in that category are CMU Tepper and Emory Goizueta.
But even if your GPA continued to track at its current level, there are very good business programs that would be accessible. You’re setting yourself up for a ton of unnecessary stress if you fixate only on highly-rejective schools and allow yourself to feel as if your life will be over if you don’t get into one of those. Even if your GPA climbs significantly, you will need attainable “safety” schools on your list, and you will have much more peace of mind over the next couple of years if you identify a few of those that you know you could be happy with. What’s your home state? There are likely good options at your public universities and/or others with which your state may have tuition reciprocity agreements. There are also some great business schools at private universities that aren’t quite so reachy - University of Denver is one example that comes to mind, as well as many of the Catholic/Jesuit U’s. And there are liberal arts colleges that have strong business programs too - schools like U of Richmond, Bucknell, U of Puget Sound, Trinity U (TX), and many more.
Identifying high-reach “dream schools” is the easy part; you can do that at the end of junior year, when you know what your stats will really look like. This year, try to set that aside (NYU Stern et. al. are not going anywhere!) and focus on identifying some schools that match your current stats and that will make good safeties even if you do achieve a great improving trend. Go on some college visits, if you can, to attainable schools, so that you start to be able to imagine yourself there. Knowing that even your backup plans can be something to look forward to is the best way to lower your stress.
Absolutely, work to raise your GPA and widen your college options. But do it from a positive, “being the best student you can be” frame of mind, not out of fear that you’ll be ashamed of where you go to college. Fall in love with a couple of attainable schools first, to neutralize that fear. And good luck with the transcript glow-up; there’s plenty of time to trend upward 