Hair care shampoo given as a gift by a friend

A friend gave it to me as a gift, so I've been using it for 3 years.

I am satisfied with using it because it makes my scalp feel cool when I wash my hair.

But it's so refreshing that sometimes I worry it might be peeling off my skin. That's unnecessary, right? Haha.

It says that it contains cypress oil and other ingredients to maintain the oil-moisture balance and supply protein to alleviate hair loss symptoms, but I continue to use it because I like the scent and the feel of it, rather than for alleviating hair loss symptoms.