It’s not the school. Before you do anything, go to the health center and see a counselor. A few weeks of therapy can make a world of difference in a short amount of time. Once things are back in perspective, then decide. Transferring when you’re depressed can risk making your depression much worse.
Also, prestige is completely overrated. Record numbers of students have applied to college in the last decade, and elite colleges have been stagnant with their capacity. This makes them look more “selective” and “prestigious” by only taking the “brightest” students, and it leads to more research grants. In reality, their getting paid for doing literally nothing. As a result, prestigious schools, who were once the standard of academic excellence have become mediocre. Regional universities have been more than happy to accept the rejects and expand accordingly, turning once third rate schools into powerhouses. This trend is happening all over the country. Examples are Central and Eastern Michigan, Middle Tennessee, UTSA, and Texas State. UTSA has literally doubled in size because of UT rejects. Just because a car is made by GM, doesn’t mean it makes the best car.