LED Matrix Leakage LEDs
Usually this sort of thing (ghosting) is caused by timing issues rather than leakage. You should have dead time between changing the column driver and enabling the row driver, and similarly should turn off the row driver before changing the column data. A few microseconds should suffice. 

But if it really is leakage then add pullups to the row driver (collectors to +5), 10K is sufficient. 

Your 15 ohm resistors are basically doing nothing- the current is being limited by the poor abused 74HC595 outputs. You're probably exceeding their maximum ratings and thus long-term reliability will be suspect.