Newspapers can be considered either primary or secondary sources, depending the way in which they are used. Ask your professor if you have questions about which they might be considered in the context of your paper.
Other libraries may have copies of other newspapers. You can use either search Worldcat or the Center for Research Libraries' (CRL) catalog to see what might be available. CRL has more than 10,000 titles from most countries of the world and every state in the U.S., including over 1,800 U.S. ethnic titles and some of the earliest African American newspapers.
If you want to find names of newspapers for a particular city, and the dates of publication, see:
Brigham, Clarence Saunders. History and Bibliography of American Newspapers, 1690-1820. 2 vols. Worcester, Mass.: American Antiquarian Society, 1947. HUNT REF-1 Z6951 .B86
Gregory, Winifred, ed. American Newspapers, 1821-1936; A Union List of Files Available in the United States and Canada. New York: H.W. Wilson Company, 1937. HUNT REF-1 Z6951 .A498 1967
You can also find other digitized newspapers by using ICON: International Coalition on Newspapers Digitization Projects