I Didn’t Arrive at Mass until the Consecration. Was I Right to Refrain from Communion?

You could have gone to Communion. The Church does not require participation in the Mass for reception of the Eucharist, so if you show up late it is perfectly fine to go to Communion. The only exception is for those who have already received the Eucharist that day—canon law does require participation in the Mass for a second reception.