"My instructor says I can't use Web sources for my paper."
Ask your instructor to clarify this, because there are really 'two
Webs.' There is the public Web that search engines find, and there's
the "invisible Web," which contains special web
sources the library buys that only the LCC community can access and
use for research.
An article you
find using a research database such as General OneFile
typically also exists in a journal in print. It's just delivered
via the Web by LCC Library to facilitate your research.