I've had unprotected sex twice, could there be a possibility i have an std or sti and don't even know? and can i go to my universities health center?

Yes/probably: There are std's that can pass to you without producing noticeable symptoms. A university health center is usually capable of providing you with these screening services.Those that may not would usually maintain a referral list of sources you could use for the service. Your student handbook may define the limits of that health centers services.