If you are invested in the brown scapular then you do not have to have the scapular blessed. The fact that you are wearing it gives it its blessing.
During the investment of the brown scapular, holy water is sprinkled on it, thereby effecting its blessing.
When I had my brown scapular invested upon me, this is what the priest did during the Rite.
A brown scapular needs an "enrollment" *if* you wish to enter the confraternity.
Otherwise, one only need to wear it, be chaste according to one's state in life, and daily recite thw Divine Office (or Little Office with permission), or Rosary.
If I'm not mistaken, in most cases, the confraternity is a loosely based. There is no registry, data base or records of Catholics who have the brown scapular invested upon us. The probable exceptions are Third Order "tertiaries" who live in a monastic community and take vows, and obviously, First and Second Order monastics.
My understanding is we "regular" Catholics (who aren't monastics) who are enrolled into the brown scapular, which is done by a short Rite that is prayed by the priest and respondent (the person being invested with the brown scapular), are spiritually part of the confraternity of Carmelites, and in order to receive the promises of having the brown scapular invested upon us, we must live in chastity according to our state in life, and daily pray the Divinum Officium, or substitute Little Office of BVM with permission from your priest, or pray the Rosary, and we must always wear the brown scapular.