Why do the characters not get high when they are injured?

It would seem that each drop of Vampire blood has a finite amount of power, so to speak, which can induce a variety of effects. Like you say, and from what we can gather from the many times humans drink V, the blood can give you heightened sense of smell, incredible strength, increased libido and heal almost any injury. However, the amount of power that can be hanressed from a given amount of V is finite and the power is applied to the most urgent need at the time of drinking, according to the True Blood wiki article on Vampire Blood.

When a human is gravely injured and is given V, the bloods power is focused, and spent, on healing the injuries, whereas if a healthy person drinks it, the power can be distributed to a variety of different things.