Well, the feeling was gone from my left hand

The story:

My interpretation: one of the bullets that had just been fired
had hit the narrator in or around the left shoulder, accounting
for his hand going numb. He was an FBI informant who had
arranged a meeting at this joint with somebody from the
district attorney's office (the "D. A. man" mentioned earlier in
the song), presumably because the FBI was investigating
corruption in the local D. A. office.

Having the D. A. himself at the scene makes things a bit more
complicated. In the US the D. A. prosecutes crimes but
doesn't investigate them (that's what the police are for). For
him to show up at the scene of the crime that was just
committed strongly suggests that he is, in fact, corrupt. But
he has to pretend to care about the FBI informant who may
or may not have been shot.