Librarian backround check & other than honorable discharge?

There should be no problem if u are upfront about your discharge. Also depending on the "patterns of misconduct" the army can not tell anyone what really happen. Also look at your discharge paper, I think on the bottom right hand side should have have a re-enlistment code on it. Look up the code and it will tell u if u could re-enlist or not after a few years. If the code says u could re-enlist that u have nothing to worry about. Go for it