How long has this been going on?
Are your eyes gritty feeling?
Are you eyes painful?
Does the redness go away?
IS you vision effected?
Alright then, It appears that you have dry eyes. Sometimes that just occurs but sometimes it is due to allergies or certain medications.
You would be safe to use Visine or similar over the counter product for dry eyes. It will help lubricate your eyes. You can use about 3 times a day if you would need to. Try not to use more often than you need or have symptoms. If it continues past a few weeks than I would see your eye doctor.
Have a great day!