All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
If you have not performed the obligatory Hajj and you are able to perform it, you must do it immediately. There is no Sharee‘ah objection to your Hajj because, as we understood from your question, you are the guarantor of your brother's debt and this is not an impediment to Hajj. Also, this is not an impediment to travel for you unless the time of payment is due and he is unable to repay; in this case the bank has the right to prevent you from traveling. Muslim jurists stated that if the indebted person and his guarantor want to travel, the creditor is entitled to prevent them or one of them from travelling. The creditor has the right to prevent the indebted person or the guarantor (Kashshaaf Al-Qinaa’).
It should be noted that it is not permissible for you to guarantee the loan of your brother since loans in the west are usually Riba-based. This would be cooperating in sin and transgression. Allaah The Almighty Says (what means): {And cooperate in righteousness and piety, but do not cooperate in sin and aggression.} [Quran 5:2]
Allaah Knows best.