My Mums Yorkshire Terrier Has A Bloodshot Eye,how Can I Treat It?

Your little dog may have conjunctivitis-a superficial bacterial infection of the eye.  It can cause green/yellow discharge and redness of the white part of the eye.  Some dogs can be painful and will rub at the eye.
It is important to have your dog see a veterinarian to have the eye stained with Fluorescein to make sure the cornea (outer surface of the eye) is intact and there is no corneal ulcer.  If there is no ulcer present then an ophthalmic antibiotic with a steroid can be used.  Steroids can only be used if the cornea is intact; steroids will really help reduce redness and discomfort while the antibiotic will treat the infection.

Try putting a warm tea bag on the eye.this will sooth the eyeball.

If it is only bloodshot, they make eyedrops for dogs. If it persists I would consult a veterinarian as it could be something more serious. I hope all goes well.

Get a warm rag and put in on it eye or go to the vet and get an eye treatment  feal better doggie