Have I sinned by pouring Zamzam water on a woman who pushed me while I was filling my bottle, and what should I do to atone for my action, considering that Allah Almighty says: "So there is to be no sexual intercourse, no disobedience, and no disputing during Hajj"?

You erred by retaliating against the woman in kind and worse. You should have applied the verse: "Nor can goodness and evil be equal. Repel (evil) with what is better." (Quran 41:34) or retaliated in kind without exceeding, as Allah says: "And if you punish [an aggressor], then punish with an equivalent of that with which you were punished." (Quran 16:126) Since time has passed and you have repented, and you cannot reach her, it is sufficient for you to seek forgiveness for her and supplicate, and to seek forgiveness for your sin. Your Hajj is valid because sins do not affect the validity of Hajj, even if they affect its reward.