Is drawing close to a sick young man to help him and alleviate his pain, while preserving one's honor, consideredzina (unlawful sexual intercourse)? And what is the optimal behavior towards this young man in a work environment? Is repentance, seeking forgiveness, and fasting sufficient for the forgiveness of this act?

You must avoid the mistakes the questioner made, starting from her conversation with the man about sexual matters, all the way to her attempts to cure him. These matters are enticements from Satan. It is impermissible for a woman to speak with men except out of necessity, with modesty and dignity, and without speaking seductively, as stated in Allah's verse: (Then do not be soft in speech [to men], lest he in whose heart is disease should covet, but speak with appropriate speech). What happened falls under figurative zina (adultery), due to the Prophet's (peace be upon him) saying: (Indeed, Allah has decreed for the son of Adam his share of zina, which he will inevitably attain. The zina of the eyes is looking, the zina of the tongue is speaking, the soul wishes and desires, and the private parts affirm that or deny it). It is from Allah's mercy that He opened the door of repentance and forgiveness for whoever repents, believes, and does righteous deeds. Therefore, she must increase her good deeds, cut off contact with the man, and avoid mixed-gender work environments.