Stop feeling guilty. She's the one who said that there was "nothing to work out" when you tried to halt the breakup. This is not your doing. You had the good sense to stop and take inventory of what was going on around you and what was best for you at this point in your life--and guess what--a relationship with her wasn't it.
If she truly just "fell in love with you" as she says (which I am inclined to suspect was a case of "uh-oh...I don't have a boyfriend anymore) then she will understand your time alone and be at peace with it until you get everything else in your life straight.
There are very few personal problems that cannot be solved with a suitable application of high explosives.