As the Acts, chapter ten, account points out Cornelius was sent by an angel to find Peter the day before Peter was informed by vision what had already been put into force.
What Peter would loose would be the thing already loosed (or bound) and that is the sense of the Greek. (Matt. 16:19-21)
Since the Greek doesn't have tenses in the way the English does the tense expressed is often misplaced.
The sense of the Greek is of an action begun in the past and is or has effects continuing into the present.
Try googling “dedemenon greek” for some better explanations.
So no, the binding and loosing was not forgiveness of sins.
As to the kingdom being “within”, I assume you mean being a condition within us as individuals, but I think that is a misunderstanding what the kingdom is and what was meant by “within”.
There must be a spiritual change in anyone who enters the kingdom, he must be re-born. Once a person has made the profession of faith, he lives as a called disciple and that entails abiding faithfully in the Word of God and obeying Christ’s commands.