I have a broken blood vessel inside my eye. The optomologist used a laser for repair. How long will it take to improve my blurred vision?

Depends. The blur is probably due to blood in the vitreous which can take weeks or months to be absorbed.
Could be a while. Often the laser seals the defect but blood and edema fluid must be resorted before the vision recovers. This can take a while! and recovery depends largely on how much damage was done by the alteration in blood supply in the first place!