Does the presence of my name as a guarantor for my brother's loan prevent me from performing the Hajj pilgrimage?

If you have not performed the obligatory Hajj and are capable, then you must perform Hajj, and there is no religious impediment. Your guarantee of your brother's debt to the bank is not an impediment to Hajj or travel, unless the debt is due and your brother is unable to repay it, in which case the bank has the right to prevent you from traveling. Jurists have stipulated that a creditor may prevent the debtor and their guarantor, or either of them, from traveling. However, it is not permissible for you to guarantee your brother for an interest-based loan, because it falls under cooperation in sin and aggression. Allah Almighty says: "And cooperate in righteousness and piety, but do not cooperate in sin and aggression."