Peace be upon you and God's mercy and blessings.
Lady Fatimah (peace be upon her) is infallible in the complete sense, free from all sins and transgressions, and there are many evidences for this.
It is agreed among interpreters that the verse of purification (Ayat al-Tathir) refers to those included under the cloak: the Prophet (peace be upon him and his family), Amir al-Mu'minin, Fatimah, Hasan, and Husayn (peace be upon them).
The preposition in the phrase "to remove all impurity" in the verse indicates a complete negation of all forms of impurity, and there is no evidence to limit this to a specific type of impurity.
Amir al-Mu'minin (peace be upon him) said: "The Messenger of God (peace be upon him and his family) told Fatimah: 'God is angry when you are angry and pleased when you are pleased.' If her anger aligns with God's anger in all situations, and her pleasure aligns with His pleasure, this means that her reactions are in accordance with divine standards at all times, indicating her infallibility (peace be upon her).
Furthermore, the Prophet (peace be upon him and his family) said: 'I am leaving among you what if you hold fast to it, you will never go astray: the Book of God and my family, and they will not separate until they come to me at the pond.' Fatimah (peace be upon her) is part of the family, and holding onto her is like holding onto the Quran, which is free from error; thus, she is also infallible. If she were not infallible, holding onto her would contradict holding onto the Quran, which goes against the command to hold onto both.
May you be successful in all good.