Pixel I refer you to the multiple posts on this thread about the many different ways in which homeopathy can seem to work.
Placebo effect - Just being given a pill by (what seems to be) a medical professional can make people get better in some cases, this is proven
Regression to the mean - over time, everything tends to revert to the average
Self-limiting illness - lots of illnesses would get better and go away regardless of any 'treatment', the fact that they get better AFTER homeopathic treatment does not mean they got better BECAUSE OF homeopathic treatment
etc.
You did not have proof that homeopathy CURED the warts, you just had the coincidence of time. For proof, you would need to show that it works in a double-blind test - i.e. you give one group of patients homeopathic 'treatments', another group a placebo, and see if there's any difference in recovery. The person giving the treatment must also be unaware of which group each patient is in (hence 'double blind'). Homeopathy has been put to this test and has failed every single time. Of course it has. There is no possible way that it could have any effect, it would violate every law of physics, biology, and chemistry.
The 'detailed questions' about your life are there to make you feel better, like someone is paying attention to you and really cares, and is giving you a personalised treatment plan.
In fact they are giving you pills made of sugar, which have been dipped in water. That's it. Really, literally. In 2010 many protesters swallowed bottles and bottles of homeopathic 'remedies' in public in order to show what total nonsense it is news.bbc.co.uk/1/hi/8489019.stm
Also incidentally, no one who was actually sceptical would have bothered with the treatment, so (not meant in a nasty way) you weren't really very cynical at all 