Has my 3.5 GPA freshman year ruined my chances at a top college?

I go to a private prep school. Unfortunately, my grade school didn't prepare me at all. It was a joke for me and I never really learned how to study...which affected me a lot this year. But I'm kind of stressing right now because I feel like I can't my GPA much and I definitely can't get a 4.0. I found out that the highest I can get is a little over a 3.8, which isn't fantastic...and that's if I get a 4.0 soph and jr years. If I do, though, will my improvement over time also be taken into consideration/stand out? I'm willing to work as hard as I can...my dream school for a long time has been UChicago...and I feel like it's a pipe dream now. Help?