Well... of course I can’t tell or tell you what you should do, but at the risk of telling you stuff you already know, I can tell you why you might do it.
The (proven?) theory behind icing is to reduce swelling. So like sprained ankles or some other injury like that gets iced so that the swelling goes down. In those cases, the swelling is not caused by infection, but (I think) by fluid in the body helping to immobilize the injured part/appendage and limit the range of motion, giving it time to heal. That way you can’t fully move whatever the injured part is, and cause worse injury.
Heat and massage are better (than ice) for fighting a localized infection. The heat helps encourage blood flow to the infection, allowing your immune system/white (?) blood cells to fight it. Massage helps break up whatever would be growing in there, and spread out, at least a bit, so that again, more blood can pass over and fight/kill off infection.
Pretty sure that’s the theory behind those two approaches. So, if infection is the problem, I’d think heat and massage would be the way to go. With that in mind, I’m no doctor, and wouldn’t be qualified to give anyone medical advice. Hope it goes away quick. You could also trace the outline of the swollen area with a pen, so you can tell if it is spreading/getting larger, or going away over the course of the next 12-24 hrs. Don’t hesitate to have a doc check it out.