Burnt pins in Macbook Pro Charging port and Charger

Two of the pins in my Macbook pro charging port and charger look burnt. I'm facing charging issues. The charger is working only after repeated tries and gets heated up. Past few days, it stopped working completely, just goes blank or stays in green light.

What are my options?

Do I have to replace both charger and charging port in the laptop? This was suggested in the Apple authorized service center, but replacing both was costly.

Is there any other option?

Can someone also explain why this burning is caused?