I have already had a hydrocortisone injection in my shoulder for impingement syndrome 2 months ago, the pain is coming back.

Need to look: If you have recurrent pain after a subacromial injection for "impingement" you may need to better discern what is causing the pain and if it truly is impingment. If you have not tried therapy that is also a good next step. You may require an ultrasound or MRI to look at the rotator cuff. You are a bit young to have any kind of cuff tears which is why i would make sure the diagnosis is correct.