Conscience is an act of appetition, and not of feeling. In a healthy person, the judgment of conscience supports the feelings and the feelings support the judgment. The extent of the feelings depend on the somatic constitution of the person. When we follow our conscience, we follow the judgment of reason and not that of our feelings. It is possible that the judgment of conscience can be correct even though the feelings seem to tell us otherwise.
Conscience is binding because it is tied to synderesis.
Since the conscience is the conclusion of a syllogism in which knowledge is applied, we must distinguish between the act of reason in applying and the act of reason in issuing a free choice. The free choice may be wrong if it chooses something the conscience told it to do. Conscience has an administrative and judiciary power but it doesn't have a legislative power. It doesn't create the norms. It conducts the interiorization of the objective norm, making it a subjective norm.