Is Trotter a Dr???

My buddy told me he believed Trotter was a doctor. At first I though he was crazy but now I'm not so sure. Why would his wife have asked for him as a dr in the club? She wasn't amused by him being at the track, and he's never usually in there. Very confusing scene. He seemed like he had an attitude about himself being much better than his other friends in the bar/track. Why is he trying to reform so much at the beginning? His house seemed too nice for a cabbie who always loses at the track. Did he have to secretly drive the cab to support his vice. Am I just overthinking it? Please help.