All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
It is not permissible to work in interest-based banks, as this involves a form of cooperation in sin and aggression. Allah Almighty says (what means): {...And cooperate in righteousness and piety, but do not cooperate in sin and aggression...} [Quran 5: 2]
In fact, engaging in interest-based dealings is one of the greatest sins. Interest is prohibited by the Quran, the Sunnah and the consensus of scholars. The salary you get from this work is unlawful, and you are not permitted to benefit thereof. Rather, you must get rid of it by giving it to the poor and spending it on Muslims' public interests. In the meanwhile, you have to leave this job and look for another, lawful one.
This unlawful money must not be used for performing Hajj or ‘Umrah. Many scholars explicitly stated that performing Hajj or ‘Umrah with unlawful money renders it unacceptable (rewardless). This is based on the hadith in which the Prophet, sallallaahu ‘alayhi wa sallam, said: "Allah is Good, and He accepts only what is good."
Commenting on the hadith, the prominent scholar, Al-Abiyy said: "Hajj via unlawful money is valid, in terms of absolving one of liability for the obligatory Hajj, but it is rewardless."
Allah Knows best.