We can safely say that part is added by the writers of the show. Even in old movies on Mahabharata, this treatment episode by Nakula and Sahadeva is not shown. Indra was not merciless to leave Karna wounded. Since Karna was following his vow of keeping his word and charity, Indra gave a boon to Karna that even after his body is cut while peeling off armour, it would not leave any scar. Karna didn't feel pain while peeling off armour or ear-rings due to this boon.
From Manmatha Nath Dutta's English translation of Aranya parva Mahabharata chapter 308: (emphasis mine)
Karna said :
- Notwithstanding it is so, O adorable one, give me an infallible dart, destructive of a heroic person, wherewith 1 can kill a mighty (foe).
- Cutting the ear-rings and the mail from my body, I will give them to you. But let not my limbs, thus wounded, look ugly.
Indra said :—
O Karna, since you are desirous of observing the truth, you will not look ugly
nor will there be any scars on your body.
O best of speakers, O Karna, you will be again endued with the complexion
and energy of your father.
- The gods, the mortals, and the Danavas, seeing Karna cut off his own body,
began to roar like lions, because no signs of contortions were visible on his face.
From Kisari Mohan Ganguli's English translation of the same chapter i.e., chapter 308 of Aranya Parva:
I shall, on my part, bestow on thee my mail and ear-rings, cutting them off my person. Do thou, however, grant that my body, thus wounded, may not be unsightly!' Hearing this, Indra said, 'As thou, O Karna, art bent upon observing the truth, thy person shall not be unsightly, or shall any scar remain on it. And, O thou best of those that are graced with speech, O Karna, thou shall be possessed of complexion and energy of thy father him self...........And Karna betrayed no contortions of face while peeling his mail.