I would use "intense" in the first and third sentences, and "intensive" in the second. "Intense" is a synonym of "strong" when used to refer to the quality of an experience or of a cause. It is not a synonym of "strong" when referring to a person or a material. The chemical rinse is said to be strong because its effect is powerful, so you may call it "intense".
"Intensive" in this context means "showing great effort or care" and makes sense to apply to work, but not to a chemical rinse or an itch. By the way, "intensive" has other, more specialized meanings in education, economics, agriculture, physics, and grammar. These are actually the main uses of the word.