Resistance makes Heat..
The MOST likely cause of the Melted Plastic around the Port/ Connector is Resistance.. Just like your Toaster, Resistance builds heat.. if the connection was not Good (both the cable and the computer) then Heat would be generated in some amount.. The worse the connection, the more the Heat created, and Damage caused..
There is NO reason that cleaning with Rubbing Alcohol or Distilled Water should harm it, of course it should be dried completely (would only take minutes, and/or some warm air flow to help) before re-connecting the Charger to it.. I quite often will hold the connector of mine to the back of my hand, or my face, to see if it is getting warm.. it really should ONLY be Warm, not Hot!!
A bad connection is really limiting many things, and by definition the resistance will breed MORE resistance as it has to work harder IF there is heat generated and the computer is under heavy load/ the battery is depleted.. (no different than driving your car with the brakes applied; the more you Brake the more GAS you need to supply to keep the Speed up.. very counter productive, and damaging!!)
Also, I suspect that if the Power Supply IN voltage is not up to the proper amount, that the draw will likely be heavier as well.. ** I cannot say this is absolute, but on many electronic instruments this is the case!!
First thing is to make sure the Cable End and the Computer Socket are clean.. then see your Apple Dealer.. maybe there is an explanation/ known issue if you are lucky.. Apple WILL NOT want you to have a 'fire breathing MBP' no matter what, if that is the case.. Good Luck!!