I have a skin tag at my waistline that has become very swollen and painful over the past two weeks and is now oozing pus, red around it and blackened.

Bad place for a tag!: It sounds like you have a common problem that has become inflamed and infected. First, you'll probably need to get antibiotics for the infection (redness, heat, pain, swelling, and pus). Then, you'll need to have your fp snip that thing off. It will continually be irritated (red and black) by your beltline rubbing it, and may simply be removed with Ethyl Chloride numbing and scissors snipping.

Remove it: See a surgeon who can probably remove the tag using local anesthesia in the office. Since the tag is on the waistline it will be a source of continuing irritation.