Is the questioner considered veiled now or not, and is expiation required of her, after she decided to veil and her mother informed her of the necessity to wait until she buys suitable clothes?

Allah has forbidden women from displaying their adornment (tabarruj) and commanded them to observe hijab (definition). A woman is considered to be observing hijab if she resolves to wear it and does not abandon it in the presence of non-mahram (definition) men or when going out. There is no specific expiation (kaffarah (definition)) for abandoning hijab; rather, sincere repentance is required, along with ceasing the sin and resolving not to return to it.