3rd degree burn you wouldn't be able o feel the area due o the nerves being dead, but it does sound like a good 2 nd degree burn.
I'd use antibiotic ointment until you can get either aloe, calendula cream or noxema (has silver sulfate in it). Keep the area moist with one of those ointments. Use 4x4 pads like suggested above and/or a gauze wrap. You can cut a sock up to put over your hand to hold the bandages in place.
burns stink. We've dealt with hospitalization worthy burns in our home. No fun.
Also, (per our plastic surgeon we worked with) don't pop the blisters. Let them pop on their own. If they pop it'll open he area up for infection.