Have you been told that only the Mass intended for a specific Sunday or holy day of obligation counts for the satisfaction of your obligation to attend Mass on that day? If so, I’m afraid you’ve been told wrong.
Canon 1248 § 1 states that one who “assists” (or “attends” or “participates”, etc.) at a Mass “in a Catholic rite … satisfies the obligation of participating in the Mass.” Notice, there is no requirement in the law that the Mass be the “correct” Mass for the day, or that it be celebrated licitly (or that it be celebrated in a church, or on a certain type of all altar, concerns that at various times in history impacted satisfaction of the Mass attendance obligation), in order for assistance at that Mass to satisfy one’s Mass attendance obligation. It only has to be Mass “in a Catholic rite”.
Sure, priests are supposed to say the ‘correct’ Mass for the time they are celebrating, but the choice of which Mass to say is a matter of liturgical law, while Mass attendance obligations are a matter of canon law. The faithful have virtually no control over a priest’s choice of Mass, or about how he celebrates it, and so they should not be, and are not, held hostage by a priest’s choice of rites in fulfilling their own attendance obligations. This point was made during the revision of the canon law and the Mass attendance norm was revised with this concern in mind. As a result, the CLSA Comm (1985) 854 said, “Participation in any Eucharistic celebration fulfills the obligation” and, in even more detail, the CLSA New Comm (2000) 1445 says: “The precept [of attending Mass] may be satisfied at any Catholic Mass, i.e., not only when the texts are those of the Sunday or holy day. For example, attendance at a wedding Mass . . . on a Saturday [evening] fulfills the Sunday obligation.” Okay?
So, get to Mass for Sunday (even if it’s not ‘Sunday’s’ Mass), and get to Mass for Immaculate Conception (even if it’s not ‘Immac. Conception’s’ Mass), and you’ll be fine.