I have an eight month old Shih Tzu which we had as a rescue only recently but late yesterday I noticed his left eye was slightly blood shot. This morning the white of his eye is almost completely red! Any suggestions what it could be? Should I take him to the vets ASAP or wait to see if it improves? My only worry is that because we have only had him a very short time, I havent got round to insuring him yet (very foolish I know and probably to my cost)

The pup is his usual happy, energetic self in every other way and at first I thought that maybe he had hurt it while playing with my other dog.

Take him to the vet as soon as possible. Any delay with eye problems can result in serious problems. It may be nothing or it may be something very serious where delay could result in him losing his sight or even his eye.
Don't want to be alarmist, but better safe than sorry!