Ouch ingrown nails. Had an old school podiatrist repair the one on my left foot, and he did it correctly -- never a problem since (20 years ago). My right foot gets one every year or so that I need to see the podiatrist for. I don't think he's completely killing the nerve bed or something. Keeps coming back.
Maybe I will get the family doc (old school Osteopath) to fix it.
I've had two done over the years, and during the last one, had a conversation about success rates with the podiatrist.
First, it is important that the cauterization procedure not be performed while there is an active infection. This is because the local will not be effective, so it would be incredibly painful. So if you've got a bad ingrowth, it will need to be cleaned up and then you'll need to return in a few weeks after any infection has cleared up.
Second, while there are several methods of destroying the nail bed to prevent regrowth of that curved edge, many (laser, thermal and electrical in particular) have low success rates (think 50% or less). My podiatrist explained that phenol was the most effective, BUT he felt it was very important to use disposable phenol kits, because while bottled phenol could be much cheaper, it has a poor shelf life, and anything other than a fresh bottle greatly increases the chances of a return.