"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" that contains special, restricted web
sources that only subscribers like the TCNJ community can access and
use for research.
An article you
find using a research database such as Academic Source Premier
typically also exists in a journal in print. It's just delivered
via the Web by TCNJ Library to facilitate your research.
So long as you know how to evaluate what you find on websites, they can be a very valuable resource.