Is protein injection possible?

It certainly is possible; a snake bite is an example of injection of mostly proteins.

Another example is an injection of vaccine against most diseases.

Whether it is a good thing or not, is another matter. Injection of the wrong protein, even a protein that is safe to eat or spread on your skin, might easily kill you. For example, a blood transfusion is mostly protein and if the blood type is not properly matched to your own blood, the transfusion probably would kill you.