I have a 58 day old Shih tzu, he is having a problem pooping , he goes just it seems like he is not done. At times blood come at the end of his job. Took him to the vet and he was OK at check up . Does anyone know what it could be.

He is not OK if there is blood in his stools. Either insist on better answers from your vet or try another one.

I agree completely with labman. Your dog may have worms, intestinal parasites, or have ingested something that is either creating a partial blockage or has perforated his bowels. If there is blood in the poop, it can be anything that is causing it, but you need to understand that this is not normal. Neither is the straining to poop.