I had my nose cauterized two days ago, and I, too, am experiencing similar symptoms: sore nose (made worse when I lean over, which sucks because my job involves pulling trash like constantly); constant drippy nose for the first 12 or so hours after the procedure, which has now mostly changed to dry stuff plugging my nose, and some ugly black stuff at the edge of my nostril (is this blood or the medicine stuff?); and sore teeth under the nostril that got cauterized.
I'm glad to hear that I'm not alone in having these symptoms - the doctor didn't really tell me what to expect after the procedure, just that I wasn't allowed to blow my nose for a few days (which drove me absolutely nuts when my nose was running like crazy!) - and I was starting to get worried about the pain, especially the pain in my teeth.