What is the legitimate Shariah solution for exiting the predicament of the usurious loan that the questioner took to help his brother pay off his debts, knowing that the brother's shop does not generate profits that cover the loan, and the questioner feels guilty?

What you have done by borrowing with usury is forbidden by Islamic law and devoid of blessing. You must repent, feel remorse, resolve not to return to it, and increase your seeking of forgiveness and good deeds.

As for the money you gave to your brother: if you did not intend it as a donation, you have the right to demand it back. If you intended it as a donation, you do not have the right to revoke it, for the Prophet, peace and blessings be upon him, said: "The one who takes back his gift is like a dog that returns to its vomit."

As for your brother's coldness and his lack of appreciation for your help, this should not be a reason for cutting ties. You will be rewarded for maintaining kinship with him and for enduring his coldness. "You will continue to have support from Allah against them as long as you remain steadfast in this."