Must I offer a sacrifice after I intended to rely on the sacrifice of the Messenger of Allah, may Allah's prayers and peace be upon him, on behalf of his Ummah, and I cut my hair, then I became able to afford the money one day before Eid?

The Udhiyah (sacrifice) is a Sunnah, not obligatory, according to the majority of scholars. Therefore, whoever is able but does not offer it, does not incur sin. If funds become available on the day of Eid or during the days of Tashreeq, and you are able to offer the Udhiyah, then it is prescribed and you will be rewarded for it. It is incumbent upon whoever intends to offer the Udhiyah to refrain from cutting their hair or nails from the beginning of the (first ten days of Dhul-Hijjah) until they have slaughtered their sacrifice.