If we sell all we have and give it to the poor, won't that make us poor too?
Yep, quite possible - at least in individual cases. Not all of us are preoccupied with our possessions to the point of forsaking our salvation as was that young man in the parable.
That’s not what Jesus was implying. He was showing him that he put his riches above seeking God.
Mark 6:33
But seek first His kingdom and His righteousness, and all these things will be given to you as well.
That goes for the rich and poor.
"Where you treasure is there your heart will be also." It depends on your definition of rich and poor.