If you are a new creation you are not at the same time an old creation.God in His wisdom has allowed each believer our dual capacity.
The old sin capacity that we are told is dead and cannot produce righteousness.
And our new capacity (new creation) that can serve God with righteousness.
Not your righteousness but serve God with the very righteousness of Allmighty God, God's righteousness. You don't see this?
You have no righteousness that was not given you. And if you attempt to produce righteousness thru obedience to the law you have disregarded the imputation of what was required to serve to begin with - the righteousness of Messiah.
And, there is nothing wrong with obeying God.