A common cause of a red eye is a subconjuctival haemorrhage, this is due to a break small blood vessel at the front if the eye. The blood builds up behind the conjunctiva and in front of the white sclera of the eye. The bleed can be small or go all the way round the iris of the eye. You should have your blood pressure checked and ensure you do not have diabetes. These small bleeds are also more common if you take blood thinners such as warfrin, are older and or take steroid medication.
Steriod treatment can increase the pressure in the eye, leading to glaucoma if used long term. There for it is important take the eye pressure using goldman applanation tonometry before steroid treatment is used, e.g. for arthritis.
If the red eye is caused by trauma you will definately have to see us asap to check your eye further. below is an image of a subconjuctival haemorrhage: