My professor says I can't use Web sources for my paper.
Ask your professor to clarify this, because there are basically 'two Webs.' There is the public Web that search engines find, and there's the "deep Web," Web sources the library buys that only the UI&U community can use.
An article you find using an online article database such as Academic Search Premier also exists in a journal in print. It's just delivered via the Web by the library to facilitate research.
Go with the strengths of the public Web
to obtain information on colleges, museums, non-profit organizations, or companies
for very current information such as news, sports scores, weather, stock quotes
to research a well-known event or individual
to use online job postings, shopping, auctions, or travel services
for opinions on a topic
to find government information and special reports from organizations
and think! There are better places to look than the public
to find articles in scholarly journals
to find articles published in popular magazines
to search databases that index articles in many academic disciplines
to find books on your topic
to locate the full text of articles or books that are copyrighted