Would a cortisone injection be solution for shoulder impingement syndrome?

Yes: Many shoulder impingement sypmtoms are due to dys-synchronization of the shoulder muscles. See a pt or physical medicine doc to get more guidance. This rehabilitation is very slow but well worth the effort. Cortisone injections work well for certain type of bursitis involving the shoulder but work best in combination with therapy as above.

Quite often: A steroid injection is a very common cure for shoulder impingement syndrome. Some times oral steroids, nsaid's and physical therapy are also needed. Probably the most important thing is time. This typically take 6-12 weeks to resolve once treatment begins. Ice and activity modification, in combination with the above treatment modalities, often solves this problem. If not, MRI may be needed.