Is the failure to buy a suitable school uniform for the mother and sister considered "unjust" to the other siblings, and is it permissible to use the bag and shoes that were bought for me?

It is obligatory to be fair among children regarding what exceeds the obligatory maintenance, and it is not permissible to favor one child over another except for a need that the other did not have. Therefore, the parents must give your siblings the same as they gave you; otherwise, it is not permissible for you to benefit from what you were exclusively given, and it becomes shared between you and your siblings. However, if these items were bought for you because they suited you, and similar items will be bought for your siblings later, then there is no harm.