Freshman year is an adjustment, no matter how you slice it. Living away from home, adapting to a new environment, adjusting to higher expectations and a more intense workload, managing time— not uncommon to have some growing pains. Treat yourself kindly.
However, I will say that I have known freshman that had a hard time getting used to a place, decided to transfer, and then started to feel more comfortable at their original university right at the end of their freshman year- but apparently they had committed to transfer. One girl left and regretted it initially, though eventually adapted to her new school. The other girl left, found great academics at her new school but found it socially difficult. She wound up returning to her original school. So really think this out and try to figure out how much of your feeling is about being in a new, unfamiliar place, missing home, versus how much of it is SPECIFIC to characteristics of the institution you are at. Are the friends you’ve made typical of the place, or are there other groups of people you could get to know? Is the campus comfortable for you? How do you like your classes? Are professors accessible?
Institutions do have their identities. I know a student who majored in English at a very traditional Ivy League college who would have fit in better at an edgier institution. I know a “third culture kid” (American raised abroad) who could not adjust to a frat and football focused liberal arts college in a rural town. Sometimes the fit doesn’t work. But give your current school a chance, and don’t reject it unless you can identify why.
Look at your academics; think about the courses you want to take; determine if you can achieve your goals at your present school. Seek out help- from fellow students, from professors and TAs, and reach out to counseling services- this is what they are here for.
As for the loans, that is another issue altogether. You will have to pay them back so make sure they are affordable. If you feel you are going into unaffordable debt, I would think twice. Remember- kids get into med school from SUNYs.
I agree with other posters that you can always apply to transfer but not accept the offer unless you feel enthusiastic about it at the time. However, the fact that you mention transferring to Barnard or NYU has me a bit concerned because they are VERY different schools. The kind of person that would thrive at a large, decentralized school like NYU might not be one to appreciate the more intimate, single sex education of Barnard. Have you narrowed down a major yet? You need to investigate the departments at your target schools.
A final thought: would it be feasible to put in an application to the school you regret not attending?
Wishing you strength.