What you describe is most likely an external hemorrhoid. This is essentially a vein, the wall of which has weakened resulting in a protrusion forming in the lining of the vein. When this happens, blood that normally circulates smoothly through a tubular shape encounters the abnormal cavity. At this point it is called a thrombosed external hemorrhoid.
In this cavity, the blood can begin to circulate, akin to a pool and coagulate forming a blood clot. When this happens, the asymetrical bump you describe becomes pressurized with blood from the clot. This is a painful condition because the area is filled with pain receptive nerve endings.
Thrombosed external hemorrhoids can, over a period of weeks, resolve the clot on their own. However, during this time, you should treat it with conservative measures such as sitz baths.
The rubber band treatment you asked about is called rubber band ligation and is typically used for internal hemorrhoids. You have the option of having your external hemorrhoid surgically cut and the clot extracted, although after a few days, most doctors will recommend the conservative approach. As a last resort, an external hemorrhoidectomy can be performed.
Preparation-H is a temporary symptom relieving product and will do nothing to alleviate the condition long term, although will help with pain and a bit of the inflammation.
There are lots of approaches to dealing with this. Educating yourself about the condition and the treatment options is your best bet. Visit my site at: Hemorrhoid Treatment Answers for detailed information on all aspects of this condition.