Chosen Solution

Please help I need to fix the gold prong inside my headphone jack

Just replace the whole jack, much easier.

You can retention them without taking apart, find a piece of fine gauge spring steel, something will hold its shape and make a hook. Try to hook the prongs and bend them into where the plug would sit, turn phone off before hand. I did this on an old phone and it helped, although I ended up just replacing the daughter board.