Is it permissible for me to continue fasting on Mondays and Thursdays despite suffering from anemia and heavy menstrual bleeding, and my mother's objection, knowing that I do not feel tired and see it as a way of drawing closer to Allah?

Filial piety takes precedence over supererogatory acts of worship. If the fast does not cause harm and the mother can be persuaded, then obedience to the mother and the voluntary fast can be combined. However, if the mother is not pleased, then her obedience takes precedence, especially if her prevention stems from compassion and concern for one's health. In this case, one is rewarded for their intention and attains the reward of fasting.