Sadly, once you get the blisters, there’s not much you can do to get rid of them, aside from draining them in a relatively sterile manner and an applying antibiotic ointment and a bandage. Then you play the waiting game and hope that when the blister sloughs of, it doesn’t leave a mark. As there’s a bit of an issue on the threads w/ posting outgoing links, I’m just going to point you towards howtogetridofthings dot com and ask that you read the “How to Get Rid of Blisters” tutorial.
There’s a saying: an ounce of prevention beats a pound of cure; the next time you feel you’re about to get a burn blister (and with burn blisters, I can often feel where one is going to form) immediately apply a cooling ice/gel pack to the area (and keep it on until you no longer feel a burning sensation in that area), to prevent the blister from forming. As Stoppit has wisely pointed out, once the blister has fully formed, the ice/gel pack is largely useless. I know this advice seems like cold comfort now, but it will help stave off more blisters in the long run.