Praise be to Allah.
If the argument was not caused by you and you have tried to uphold ties with her, and she is the one who refused, then there is no sin on you, but you should carry on trying to uphold ties with her and treating her kindly as much as you can, and ask Allaah to reconcile between you and protect you from the tricks of the shaytaan.
Muslim (2565) narrated from Abu Hurayrah (may Allaah be pleased with him) that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: “The gates of Paradise are opened on Mondays and Thursdays, and every slave who does not associate anything with Allaah is forgiven, except a man between whom and his brother is some grudge. It is said: Wait for these two until they reconcile, wait for these two until they reconcile, wait for these two until they reconcile.” This is an important hadeeth that points to the seriousness of severing ties and bearing grudges, and shows that they are impediments to forgiveness.
Ibn Raslaan said: It seems that if one of them seeks to reconcile with the other but he does not accept it, the one who seeks reconciliation will be forgiven. End quote from Sharh al-Zarqaani ‘ala al-Muwatta’ (4/335).
Al-Bukhaari (6237) and Muslim (2561) narrated from Abu Ayyoob (may Allaah be pleased with him) that the Prophet (peace and blessings of Allaah be upon him) said: “It is not permissible for a Muslim to forsake his brother for more than three days, each of them turning away from the other when they meet. The better of them is the first to greet the other with salaam.”
Ibn ‘Abd al-Barr said: They differed concerning two who forsake one another and one of them greets the other with salaam – does that mean that he is no longer forsaking him or not? Ibn Wahb narrated that Maalik said: If he greets him with salaam then he is no longer forsaking him. It is as if – and Allaah knows best – he based this on the words of the Prophet (peace and blessings of Allaah be upon him), “The better of them is the first to greet the other with salaam.”
Abu Bakr al-Athram said: I said to Ahmad ibn Hanbal: If he greets him with salaam, will that be enough with no further need to speak to him? He said: That depends on whether he used to do that before he forsook him. If it is known that he used to speak to him then merely greeting him with salaam does not mean that he has stopped forsaking him, unless it is a kind of greeting that is not immediately followed by turning away.
Something similar was also narrated from Maalik. It was said to Maalik: A man forsakes his brother then he greets him first without speaking to him any further. He said: If the other man is not causing any offence to him, then that is not sufficient to end the rift unless he speaks to him and lets go of the reason why he forsook him. End quote from al-Tamheed (6/127).
Al-Nawawi said in Sharh Muslim: “The better of them is the first to greet the other with salaam” – this is the evidence for the view of al-Shaafa’i and Maalik and those who agree with them, that the greeting of salaam ends the forsaking, and removes sin from the person. But Ahmad and Ibn al-Qaasim al-Maaliki said: If he is still causing him offence, then the greeting does not end the forsaking. End quote.
To sum up, the fact that you greeted your sister and spoke to her means that you are no longer guilty of the sin of forsaking and severing ties. We ask Allaah to accept good deeds from us and from you.
And Allaah knows best.