I have an old silver trophy from a chess tournament I played in that my father took me to back around 1975.  I can't read much of the engraving anymore and I can't remember who sponsored it.
     It was held in Hampton, Virginia at Thomas Nelson Community College.  Is
there any way to look up old chess tournaments and find out information
about them?

Chess Life & Review had some tournament reports of local events like that. The local or regional chess magazine, if any, would be a likely source too.

Yes, I used to read a chess magazine back then now that I think of it.