The Power of Private Confession and Absolution

A theft from a mothers purse and the subsequent fear of punishment weighted upon the chest. I know of only one relief, confession and absolution. However, do I, as a vicar have the authority to absolve of sin? It was not a random disciple that Jesus lectured on forgiveness but Peter. Or, does what Jesus said to Peter expand to the whole body of forgiven restore people as Jesus taught in a parabolic way using an unmerciful servant as an example, with the warning do it? I am left wondering because today I was confronted with a child who was suffering from the shame and guilt of trespass. He had no words to confess to God so of course I led him by the words given to us through the Apostles. I absolved him as he believed, that the forgiveness was of God and not man. I am just wrestling, in my short-lived vicarage career, with several incompatibilities that we seem fine in glazing over, like Augustana XIV, within our vicarage experiences. So I am asking the question, is the authority to remit/retain sins a key that all believers are given on account of their righteousness or rather a specific aspect of the Public Ministry handed down by the Spirit through Apostolic Succession?