Am I obligated to continue helping my husband financially with the household expenses from my own money, knowing that he is unjust between me and his other wife?

A husband must be just between his two wives in terms of financial support (nafaqah). Justice is a condition for the permissibility of polygyny, but it does not mean equality. Rather, it means giving each wife what suffices her and her child. Financial support is obligatory upon the husband, and a woman is not obliged to spend on her household unless she does so willingly, and for that, she will be rewarded. If she spends with the intention of being reimbursed, she is entitled to that.