Of course you can transfer if you are unhappy… and if your grades have been solid so far, probably you will be able to transfer to a very good college.
But the question for anyone considering transferring is always, is it the college or is it you? Often it is at least a combination of the two.
People make their own happiness. What would make you happier at school? You ought to see a counselor at Penn and talk about your “depression/ anxiety.” These are big issues that you need to address.
It is possible that the problems that plague you at Penn would follow you anywhere else if you do not address them directly.
And the stereotypes you cited about Penn kids? Stereotype is all they are. Many kids there will match the stereotype, but many will not! I have known some wonderfully kind, down-to-earth, quirky kids who went to Penn. Everyone would call them “real” and they were more intellectual than preprofessional. And not rich. Try to get to know the people around you and value them as people. Do activities that may attract people with similar interests and personalities to yours. You will find some real friends. And that will help you feel “connected” to your school.
Also be aware that, not all, but some people you consult who do not go to an Ivy may cheer for you to transfer because they could not get into Penn and your stated unhappiness there makes them feel better. So a chorus of agreement does not equal validation that Penn stinks.
You have an amazing educational opportunity that can yield lifelong benefits both in terms of your learning now and opportunities in the future. So see if you can find happiness where you are.
If, even after becoming more socially connected and working out any underlying issues with therapy, you still feel the college is not a “fit,” of course you can transfer. People can get great experiences, and have super outcomes, from many, many colleges. It is more about the person than the name of the college.
Wishing you good luck in finding much happiness, whether at Penn or another college.