Is it possible to suffer a AA battery-related injury?

So I was just operating my…Game Boy (best used late at night in bed), and now my pinky is injured. There wasn’t a moment of sharp pain when the incident happened, but suddenly my pinky started really hurting. I waited until…the game was over to check, and the pain got really bad. When I checked, my pinky was intact but swollen and warm. When I squeeze it it stings, like a burn.

The weirdest part was that one battery was making a loud noise, and continued to make it for several minutes after being removed from the Game Boy. I was in the habit of storing this particular battery in the Game Boy with the other two but backwards, so my Game Boy couldn’t accidentally turn on deep in my dresser drawer. Thus, the coil was pressed against the wrong end for a long time.

Reckon some battery acid leaked and burned my poor pinky?