Make sure you are well hydrated both before and after exercise. I occasionally experience lightheadedness immediately after 3 miles on the treadmill when I'm dehydrated but if I remember to drink lots of water hours before the workout, I don't experience any problems.
Just to be sure, I suggest you discuss this with your doctor before resuming strenuous exercise.
Most medications for hypertension have serious side effects, u didnt mention what u are taking, try exercising without taking d medication and c what happens but i'll discuss with my doctor first cos some of these drugs are dangerous when stopped suddenly (especially the ones made from snake poison ACE inhibitors and beta blockers)