Is telling others about my brother's healing after giving charity on his behalf considered showing off (riyaa'), and is disliking riyaa' sufficient for the act to be accepted?

Your informing others about the benefit of charity for a perceived interest is not ostentation (riya'), such as encouraging people to give charity or for them to emulate you. Rather, it is a signpost to good. Similar to this is speaking about blessings as a way of thanking Allah, for speaking about a blessing is part of showing gratitude for it. Muslims used to consider speaking about blessings to be a form of gratitude for them. It is permissible to inform others about a good deed for a beneficial purpose, as Abu Bakr Al-Siddiq (may Allah be pleased with him) did when the Messenger of Allah (peace and blessings be upon him) asked him about the good deeds he had performed on that day.