What should I do, as I vowed to fast for three consecutive months if I committed a certain sin, then I committed it, and I was unable to fulfill the vow due to work circumstances and responsibilities?

Avoiding sin is a religious obligation. If a Muslim swears or vows to abandon a sin, this obligation becomes even more affirmed for them. And whoever vows to fast or perform a similar act if they commit a sin, this is called a vow of obstinacy (Nathr Lajaj). The majority of scholars hold that the person is given a choice between fulfilling it or offering an expiation for an oath (kaffarat yamin (definition)). You must repent from the sin and resolve not to return to it.