After a boil has come to a head and been drained, is there any useful treatment to apply to it? In terms of causing the redness and remaining soreness go away more quickly?
Is it better to cover the boil with a bandage? What if the boil lies where it will be repeatedly irritated by waistbands and such?
Anitbacterial ointment and a light bandage to prevent spreading.
Oral anitbiotics might be prescribed to prevent a spread of the infection.
The light dressing and petrolatum base of an ointment should prevent skin irritation, although skin can be irritated by anything without warning.
Slight Hijack…
What’s the difference between a boil and a cyst?
Thanks for the advice, Philster! I knew nothing about boils, didn’t even realize what that rapidly swelling lump meant until it burst.
Ahhh. We never forget our first ones, do we? 
Back when I was in high school I found out what a boil is. Nasty little things. It was on the back of my knee and was fairly painful at all times. Finally one day, I sucked it up and showed my Mom. She put this even nastier black gunk on it and made me do that everyday for a while. It shrunk and eventually disappeared. I have no idea what the magic tar-like stuff was but it worked like a charm.
“After a boil has come to a head and been drained, is there any useful treatment to apply to it?”
No
“In terms of causing the redness and remaining soreness go away more quickly?”
Hot compresses 3 times a day is a traditional treatment but I’ve never seen any studies showing this to be effective.
“Is it better to cover the boil with a bandage?”
No.
“What if the boil lies where it will be repeatedly irritated by waistbands and such?”
If the skin over the boil is irritated by clothing rubbing against it, then covering the skin with something will reduce the skin irritation. However, THE (accent on the THE) treatment for boils is drainage. Don’t do anything that could cause pus to accumulate inside the boil.
Nota bene - Antibiotics are not needed for most boils, but there are exceptions.