Hi welcome to Health care magic forum. As you describe it appears to be xero derma with secondary occlusion of nasolachrimal duct, or one of them. Nasolachrimal duct is a tiny duct draining lacrimal secritions into the nose so that eyes are always kept moist and and dont drible the secritions out side the eye.
Due to occlusion of the duct there is no reason why skin around the eye is dry, so so suspect it to be xeroderma
I advise you to consult an opthalmologist for diagnosis and treatment, you may need to have recanalisation of the duct, so that the secetions pass into the nose, if you get full relief well and good, other wise you have to consult a dermatologist
for treatment of the dry skin
The reason could be tensions of education or life. So i advise you to be away from the tensions, you can use a cream to keep the skin moist,repeatedly.
Take more of water, fruits and juices, sprouts, and salads, to keep your skin healthy.
Wishing for a beautiful skin, and thanks for calling.