I think I wrote the same paper some 25+ years ago, except I focused on poetry by known poets. Your project looks much more fun--and difficult! I know normally we are supposed to give answers and not point you to places to look, but since you seem to need places to look, and this is something very few American historians could spout off a list for, I will answer with some resources and tips.

First, check what newspaper databases your uni library has online. Find some American newspapers in a database from the period. Occasionally, more local papers published letters from soldiers to the families or to the newspaper. Hard to find, but there are a few out there. Can't recall much serious poetry in any, though, but does not mean it isn't out there. This would be a good source to find civilian poetry sent to the newspapers. Newspapers.com, Chronicling American from the LOC, NewspaperArchive.com, etc.

Second, look for resources like Portal to Texas History; many states have similar resources. In addition to newspapers, these sources (usually run by a major university) have some diaries scanned. What they have varies by jurisdiction. Check smaller universities like Texas A&M University-Commerce that operates the North Texas Digital Consortium across the states that were allied with both north and south.

Third, Check WorldCat. There are many books of digitized letters, but no idea which ones contain poetry.

Do a deep google and you can find collections of letters like this you can review, and it will also lead you to university resources like this one, which I believe is also available on JSTOR.

You also need to look for genealogy and local history books from areas where big companies were established, but that weren't large cities. These locally-compliled, independently published books are in most major genealogical libraries, and the Mormons, through their site, or other libraries, may have some online.

For the south, a MUST CHECK is the old volumes of the newsletters of the United Confederate Veterans. Vets wrote in letters to this publication that were truly amazing, and I have seen some poetry in those. The Dallas Public Library has this, and it is like a 20 volume set. You may be able to find it online, and some states societies have newsletters online. But you want newsletters prior to 1936 when these vets were still alive.

Email librarians in smaller libraries with archives in Southern States. Many of those librarians are still checking email from home (as I've recently discovered). They may recall something in their collection you can look for digitally. For TEXAS resources, I recommend searching:

UNT Portal to Texas History

SMU Digital Archives

UT Arlington Digital Archives

North Texas Digital Consortium

Dolph Briscoe Center for American History at UT Austin

Institute of Texian Cultures, San Antonio (they have the old DRT library from the Alamo)

and catalogues of: Houston Public Library, Dallas Public Library, San Antonio Public Library, Austin Public Library, and UT Austin to look both at what is in their stacks and what is in their archives.

REPEAT your search in other states of the South and North. The American Antiquarian Society may also have some items in his holdings. Each state has a similar collection of universities and libraries with the biggest stacks, and more active archives, which is where I'd start.

Without a library, you are hamstrung a bit as a lot of this stuff won't be digitized. However, you can Google Scholar/Google Book search the names of some of the books and see if they are quoted in other books or materials.

Without ILL services operational, you will have to rely, I suspect, on JSTOR and many other databases a good deal. Remember, too, that this is technically cross-disciplinary, so check JSTOR or other searches provided by your University for any scholarship in the English/Language arts/Literature realm, too.

This is kind of one of those projects that seems like it would require about 20 books from ILL, so I wish you the best of luck doing it digitally, and ask that you please come back and tell me in the comments how your paper wound up and what you were able to find.