I would argue that one of the principal ways in which Orwell communicates his extreme discomfort in this situation is through his narration of how the elephant dies (or doesn't die) after Orwell begins to shoot it. We are already told that Orwell doesn't actually want to shoot the elephant, but feels forced to by the pressure of the crowd and the strange way in which colonialism actually strips you of your liberty and agency. The description of how the elephant dies is agonising in the extreme. Orwell seems to shoot endless bullets into the elephant with it coming no closer to dying. Phrases such as "long rattling gasps" and the image of the side of the elephant "painfully rising and falling" with the blood streaming out of the body "like red velvet" only serve to heighten both our discomfort and Orwell's discomfort. In the end, note what he says:
In the end I could not stand it any longer and went away. I heard later that it took him half an hour to die. Burmans were bringing dash and baskets even before I left, and I was told they had stripped his body almost to the bones by the afternoon.
Orwell's own personal feelings of not being able to stand the agony he had inflicted on the elephant any more lead him to leave, underlining his discomfort, both physically and mentally.