Why do I feel light headed and dizzy after exercise?

I started exercising about 6 weeks ago. Whenever I do a hard class I feel like im going to faint afterwards, really light headed and "not here" I did a class few hours ago and still feel strange. I drank heaps of water and I have eaten. I have a history of blood clots, but have been given the all clear from that.

When someone works out, his or her heart pumps harder and faster, increasing blood flow to the actively exercising muscles. Blood vessels in the skin expand to dissipate heat. When exercise ends suddenly, the heart slows down its pumping activity, decreasing blood circulation even though blood vessels remain dilated. As a result, blood pressure can fall and a person can feel dizzy or even faint.
It can be common for someone to feel lightheaded or dizzy when s/he abruptly stops arduous physical activity. Feeling this way after exercising is probably not dangerous. However, if a person feels lightheaded or faint during exercise, that may indicate a serious heart condition. S/he needs to stop exercising and get medical attention and evaluation.
If someone feels faint, s/he needs to lie down so his or her head is level with his or her heart. Blood flow to the brain will increase, causing the feeling of faintness to abate. Maintaining good nutrition is also important if one is a vigorous exerciser.
To help limit or prevent feeling dizzy or lightheaded after exercise in general, cooling down adequately is key, coming to a full stop only after gradually decreasing activity. Slowing down in this way can help by maintaining heart rate and circulation and only gradually reducing them. In your case, you already warm down before being still, but perhaps walking briskly is too sudden a decrease in movement; jogging slowly at first before dropping down to a brisk walking pace could do the trick.
If, however, this more incremental reduction in activity does not improve how you feel after a run, or if this is a new development, it's important to make an appointment with your health care provider for a check-up and consultation.

I would suggest going to get a full physical including an EKG for your own well being. From your description it sounds like you may be experiencing severe fluctuations in your blood pressure but only your doctor can tell you for sure. The only other thing I can think of is that you have an inner ear imbalance. I hope this gets resolved quickly and painlessly for you.