According to the Ohio Dept of Health, in 2006, Hamilton Co had 42 cases of syphilis. In 2007, there were 55.
Its possible, but not likely, so don't worry too much about syphilis, ok?
You can also see gonorrhea stats on this page - http://www.odh.ohio.gov/healthStats/disease/std/std1.aspx
Aj
Syphillis is really rare in America, it is possible but your chances are really low. If you did get syphillis you would see a sore in a couple of weeks.
NGU and gonorrhea are possible but the risk again is low. The Dr's on this site say test if you have symptoms (gon-2-5 days, NGU 7-14 days). But if no symptoms no need to test unless you are worried.
You could also get herpes, but without any visible sores then herpes and syphillis is probably not a worry.
Don't do too much self examination, but if you get symptoms-discharge from penis and/or burning while urinating then see a Dr.