Magsafe Adapter 2 Overheating

Hi,

My magsafe adapter 2 overheats quite regularly when charging (the magnetic part that attaches to the computer) and gives me a lot of trouble. I've cleaned out the port and the charger, there is no debris in the way, I reset my battery settings, but am still having trouble with the connector getting incredibly hot (too hot to touch) if it charges at all. I just found that one prong in the Magsafe 2 is discolored (not indented or recessed, just burnt looking) and so is the corresponding prong in my Macbook. Two Questions- Am I harming my macbook if I charge it with this charger until I can get a new one (I rely on this macbook for work and I am traveling); and two- Did the computer break the charger or the charger burn the computer?

Note- this is the apple charger that came with the machine originally, not a third party or anything.

Thank you for any help!