Must I fast ten days as a punishment for committing the sin of masturbation after I pledged to God to do so, despite the difficulty of the matter and my repentance from this sin almost a year ago?

If the vow is in the form of a solemn pledge, such as saying: "It is a duty upon me for Allah that if I masturbate, I shall fast," then it is an oath of obstinacy and anger (nadhru lajaj wa ghadab), and the doer has the choice between fulfilling it or offering an expiation for an oath (kaffarat yameen). However, if the vow was merely a thought that you did not utter, then no expiation is required if you break it. Nevertheless, you must fulfill it due to the obligation to refrain from unlawful acts and the general evidence for the necessity of fulfilling vows, such as Allah's Almighty sayings: "And fulfill the covenant of Allah when you have covenanted," and "And fulfill the covenant. Indeed, the covenant will be questioned about."