Trust me, I'm not judging you or trying to be mean when I say this, but I thought the recovery time for a C-section was 9 weeks? If you started working out 'pretty hard' then that definitely might have triggered the heavy bleeding and dizzy spells (possible anemia?). Of course, I totally understand that your doctor may have given you the green light to resume normal activities. You should probably call your doctor since you have both heavy bleeding and the dizziness.
Please remember that your body prepared and changed for 9 months in order to bring this baby into the world. You will have plenty of time to get your pre-body baby back, so take it slowly and don't overdo things! I know we all see celebrities who are back in tiptop shape after a month but don't forget that most of them have trainers to whip their body back into shape, chefs or assistants who prepare their dinners, baby nurses and nannies to watch their newborns while they go work out for hours and actually get decent blocks of sleep.