Can eye injury cause sties?

Unlikely. I believe you mean "styes"? These inflammatory lesions originate from oil glands on the margin of lids called meibomian glands. Rarely, scarring of the lids may disturb the lipid flow and lead to styes. Blepharitis is the most common cause of styes.
No. Styes are due to changes in the glands of the skin especially at the base of the eyelashes. Injury will not cause you to get more.

Related Questions

How could a blunt eye injury cause terrible light sensitivity?

Interfere with pupil. Blunt eye injuries can interfere with the pupil mechanism of your eye. When the light is bright, the pupil may not be able to construct normally, creating light sensitivity. In many cases, this will go away over time.

What can I do for the pain and light sensitvity after eye injury cause by a cord from a pair of hair clippers its been over 48hrs redness and pain?

See your eye doctor. The injury may have caused an inflammatory condition called uveitis. See your eye doctor immediately for treatment.
Seek treatment. You could have inflammation on the cornea, an abrasion, or inflammation inside the eye. I'd recommend seeing an eye md for evaluation.