Cigarette length burn- back of hand. no pain/blisters when it happened. 3 days later, the skin/joint next to it hurts (they weren't injured). why?

Thermal injury: It's still a thermal injury, even if you felt no pain during the cigarette burn to your hand. Luckily, you did not have any blisters, which would've indicated a second-degree burn. So the joints and areas are still affected by what occurred as there is a thermal dispersion of heat in the dermis area from where the burn started. And joints and tendons can react by producing Lactic Acid to the traumatic incident.