Databases provided by your library are very different than resources you find using Internet search engines like Google.
Click HERE for the differences between databases and general web resources.
In general, if your professor tells you NOT to use Internet resources, he/she does NOT mean library databases. Library databases contain carefully evaluated material that you can trust; the web, not always.
Library databases contain many journals that also exist in paper format.
Sometimes libraries have both. The College Library owns the Journal of American History in paper AND has access to the electronic version.
You can go to the periodical shelves to find the paper version; to find the electronic, you can go to Full Text Finder and look up the Journal of American History.