The small pain in the chest of the soldier is probably from a wound,perhaps from a bullet, incurred during the war he was involved in.
The wound which causes the pain, is insignificant to the soldier because he is supposed to be brave and that is part of the risk he has signed up for, the moment he became a soldier. Thus, even though we know it is a fatal wound and he finally dies of it, to the soldier, the pain he feels in his chest is 'small' or not worth complaining about. He is breathing his last on the battlefield and is one of the last ones in the troop to survive. He has been through a long and hard night fighting a battle and now just wants a sip of water to quench his thirst. Smiling in the face of death, the soldier tries to belittle the wound that has taken his life and it is his memories of a family that's proud of him being a soldier that fill his mindin his dying hours. He is not expected to writhe in pain due to this slight wound. After all, that's what one expects from a soldier.