3 Week Period & Clotting - What's Wrong?

Hi there! I've been having some possibly major issues concerning my period and I'm looking for any feedback that might help me figure out what's going on with my complex body!  Basically, I'm in my early twenties and have never, ever had normal periods.  I started having periods at 9-10 years old and since then my periods have only lasted 3 days and have never been regular- some periods would come a week late, others would stop for 2 months.  During my period, I only have body-numbing cramps/pain on one side of my body and usually near where my right ovary is positioned.

Until recently I had gotten used to the fact that I will always have random periods (I refuse to go on 'the pill').  However, for the past month my period has changed completely and to be quite frank, I'm very worried.  As of today, I have been on my period for 3 weeks straight (21 days) and it doesn't seem to be letting up even the slightest.  While my period has been heavy for these past 21 days, what concerns me the most is that I have been having sporadic surges of blood/ blood clots.  For example, yesterday I was relaxing and suddenly it felt as though I had peed myself - I went to the restroom and it looked like a crime scene not to mention the fact that there were numerous quarter sized clots prevalent.

So I'm asking for suggestions/feedback that might point me in the right direction as to what could be wrong with my menstrual cycle.  I should warn you that I'm very modest and getting a pelvic exam is the absolute last thing that I will consider having done.  Thank you!