Can off and on severe itch be a result of pulled/broken hair. it comes when skin is stretched at those two spots on my leg?

Not exactly: if you took a scissors and cut the hair, it wouldn't itch. Itching is a skin or lower issue. The pulling of hair if it pulls on the skin might. Some people get hives/histamine release from skin being rubbed/pulled irritated (anti-histamines help). Some feel itching instead of other sensations in the skin (nerve pills help). cannot say in your particular case.