Is distributing all of the money designated for me—in addition to the amount designated for charity—out of fear of not receiving reward, a correct action that brings good to me and to the benefactor, or is it an injustice to my family?

The one who spends is rewarded for his spending, for Allah Almighty says: "And whatever good you put forward for yourselves - you will find it with Allah. It is better and greater in reward." And the Prophet, peace and blessings be upon him, said: "You will not spend any expenditure seeking thereby the Face of Allah, but you will be rewarded for it, even for what you put in your wife's mouth." However, if the spender withholds an amount that covers his needs and the needs of his family, that would be better for him, for the Prophet, peace and blessings be upon him, said: "The best charity is that which is given when one is rich, and begin with those whom you support." So, a condition for charity is that the one giving charity should not be in need, nor his family, or be in debt, for paying off debt takes precedence over charity.