as you mentioned 'very small amount of water', I presume that you do not have any kind of filter in the tank, if it is big enough to be called one. It is highly possible that the infection is caused by poor water quality, but not excluding the possibilities of injury, secondary condition from a severe parasitic infection, rough handling, stress and high pH burn. I'm not aware of any home made remedy, but I would not advise you of any medication because it is best that you find sound advice from experts, or fish diseases related websites. I have a html file with great information on this topic, and I can attach it to you if it pleases you(I have forgotten where I downloaded it). It would be better for you to understand various fish diseases, occurences and cures because fin rot is only one of the many you will encounter in fish keeping. I suggest you do a major water change to improve the water quality first before other possible actions you are to take.
One question apart from fin rot, why is Betta often kept in small tank without any filter system? Yes it has unique oxygenating system and like calm water, but a gentle fliter and bigger tank make a happier Betta, providing it a 5 stars treatment then a homestay standard that most Bettas are suffering.