If you read more of Beckett's work, you will find that every single one of his characters is, in one way or another, suffering. In his mid-twenties, when Beckett was suffering from severe depression, he began to read the philosophy of Arthur Schopenhauer. Schopenhauer proposed that the world was grounded in suffering. He believed that our individual wills (drives, desires, etc.) only bring us more pain and torment, so desire is something to be fought rather than followed. This was a view of the world that Beckett appreciated; he liked Schopenhauer's "intellectual justification of unhappiness." Suffering is a theme explored very deeply in Endgame. Beckett imagined nightmarish situations for his characters and then explored how they might deal with them. It is one of the most fundamental themes of his work.
In a world without hope or higher aspiration, the ability to endure suffering is the closest that the characters can come to human dignity. Hamm, in particular, sees the dignity in his own suffering and thus tries to emphasize how much pain he is in.
The fact that Clov has always, in part, brought his suffering upon himself by not leaving Hamm makes him feel responsible for his pain. It also makes him feel as if his own suffering is trivial compared to that of the other characters in the play.