are college names copyrighted? If I wanted to make t-shirts could I
use college names like "Rutgers" or "Lehigh"? What about state names
like "Delaware" or "Maryland"?

Copyright isn't what you need to be concerned here: a single word
cannot be copyrighted. However, one word or name can easily be
trademarked, and many college names are protected by trademarks.
Rutgers is one of them.

Oops. Sorry about a typo. Make that first part "Copyright isn't what
you need to be concerned with here."

So if I were to use the Trademarked names I would need permission from
the college itself? Or how does that work ..

Basically, were you to intend to use some established trademark for a
usage in which the trademark-holder has some involvement and/or for a
usage that would potentially cause confusion in the marketplace (for
example, by implying that the trademark holder authorized your usage,)
you would need to come to a licensing arrangement with the trademark
holder. To do so, you would contact the trademark holder (or
his/her/its designated representatives; many organizations have
licensing companies or agents to look after these matters); make a
proposal for the usage; and negotiate an arrangement.

There are, I'm sure, certain cases where you probably wouldn't need
formal permission from a trademark-holder (or could "get away" with a
certain usage) but to be certain of your particular status, you'd be
better off consulting with a real legal expert talking about the
specifics of your idea.