Of course you do. The privates you'll need a better SAT score. GPA-wise a 3.8 makes you competitive (I can only speak for my state) for UC Berkeley and UCLA.
To be honest, though...neither of those are really going to help you get a job unless you want to teach. I think those two majors were found as the least useful but to each his own. Maybe you do want to teach. I know someone who got into UC Berkeley with a 3.9 GPA in English.
Anyways, good luck. In the end though, prestige isn't everything. Until graduate or professional school.
Have a backup plan for career options. My girlfriend's brother was a Philosophy major at Brown and wound up working at my Rite-Aid. Go figure.