"give a shot" is correct and usable in written English.
It can be used to mean that you are attempting something or giving it a try. For example: "Let's give this new recipe a shot!".
Hopefully I can give a shot in the arm.
It might be outlandish, but it's something I would like to give a shot.
Minimally, the network believes the Games will give a shot in the arm to its news programs.
"He couldn't be anywhere unless there was someone around to give a shot," said his mother, Dana Collins.
If they can give a shot in the arm to our recitals, that's something we have to experiment with.
While introducing Ukrainian teams to Russian football may give a shot in the arm to match quality, few would bother to see the games in person.
She was given a shot of something, regularly, to quiet her down, and this worked.
Upon arrival at each bar, participants are each given a shot and enjoy discounted drinks.
In 1973, American International gave a shot to young director Brian De Palma.
The art department gave a shot its color scheme and general lighting.
Always consult a veterinarian before giving a shot to a cow.
