It is abnormal to feel sting in the eyes when you put contact lenses in. Since the contact lens has to contact the the surface of our eyes, our eyes may feel uncomfortable at the beinging. But it shoudn't cause sting in the eyes. If you suffered from it, it may caused by the scratches of your corneal. Or your contact lenses contain lots of bacteria or somethings that cause allergy to your eyes. You'd better make a appointment to an eye doctor.
No, it is strange to feel sting in the eyes when you wear contact lenses. It maybe normal to feel discomfort in the eyes as first you put contact lenses in the eyes. But it should not be happen that sting in the eyes. You'd better check your contact lenses if there anything on the lenses. If you not, you try again. If you still feel sting in the eyes, your eyes may allgeric to the lenses. Seeing an doctor or consult an opticain.