great update Kelly,
As for pain - if its just hot, tight, tingly that's a sign of engorgement and the fact the milk has come in and you're naturally overproducing for now. Def do the cold compresses after (I used straight from the freezer). Hot before for now will allow you to make sure you don't get blocked and get that tiny bit of milk off so Corey can latch well.
In your position, if its very tight and painful, I would take nurofen as well. Its totally safe for bf babies and will reduce the swelling as a non steroidal anti inflammatory. I took it (and even stronger NSAI with Oscar due to issues with piles and major swelling in my nether regions) for at least the first 10 days xxx