Red eye. Contacts deprive the eye of oxygen. Things you can do to prevent red eye include limiting the number of hours per day you wear contacts, trying another type of contact with greater oxygen content, avoiding sleeping in contacts, using artificial tears such as theratears to keep the eyes moist, taking one day off per week to wear glasses only, don't rub your eyes.
Get evaluated. Many things can contribute to redness while wearing contacts. Type of contact lens, solution, fit of contact lens and your eye health can all contribute. I would recommend getting an evaluation with your contact lenses to see what can be changed.