Can eye contacts cause red and itchy eyes with white discharge?

Yes, others can too. While this can signify an infection associated with contact lens overwear, a red, itchy eye with whitish discharge is quite consistent with allergies. Cool compressed, artificial tears, otc allergy drops such as zaditor (ketotifen) or alaway or prescription drops such as Pataday are all effective means of treating this.
Yes. This is often a sign of contact lens over-wear or even infection. Have your eyes evaluated by an eye doctor immediately. An eye infection is a true medical emergency.