OTS is an acronym which stands for "Off the sh*ts." It is a slang term used to described someone who's under the influence of a substance. Anyone who's high or drunk is often described as being off the shits (#OTS). This particular slang started becoming popular due to the rise of drill music from Chicago. Since most drill rappers are from Chicago, they tend to use popular Chicago slangs in their songs. Some individuals believe that this term originated from Chicago since it wasn't well known before the rise of drill music, however, this term has been used by numerous rappers way before drill rappers such as Chief Keef, Lil Durk, and Lil Mouse made it popular.
In the song 'Chiraq' by rap group 485, S. Dot says "Smoking dope - Huhhh - I'm off the shits", in the song 'Eater' by Soulja Boy, Lil Durk says "Man I'm off the shit, smoking reefer". As mentioned above, this slang has been around for a while, in Warren G's 'And Ya Don't Stop' song, he says "Past tense it's the Indo smoke - Choke, off the shit that I'm doin".