Before Jesus, people would go to Abraham's bosom instead of Hades because of their own righteousness. NT Jesus saves us who desire righteousness and we can go to heaven.
So yes, only by the righteousness of Jesus can we be with God. But this does not mean we don't have our own righteousness. Albeit as filthy rags, there was a distinct difference in hearts / desire for what is good for for example Lazarus over the rich man.
I am the vine, ye are the branches: he that abideth in Me, and I in him, the same bringeth forth much fruit: for without Me ye can do nothing. - Jesus Christ ;John 15:5