Am I liable for anything after I made a vow in a state of anger to hit my son until he bled, and I did not do it?

You owe an expiation for an oath (kaffarat yamin), because striking a child until blood flows is not an act of worship pleasing to Allah, and it is a vow of disobedience that must not be fulfilled. The expiation for an oath is to feed ten needy persons, or clothe them, or free a believing slave. If one is unable to do so, they must fast for three days. The feeding should be half a saa' of the staple food of the land, which is approximately one and a half kilograms.