Cortisone injections in your spine could cause thinning skin, bruising, or loss of pigment usually only at the injection site, not over the whole body. Since the medication is going
into the back, only a small amount of it is absorbed by the body, so systemic (whole body) effects are really rare.
I would look for another cause for your symptoms, as you are correct that it is not normal for someone your age to have this issue. Are you taking oral steroids (like prednisone)? Are you on a blood thinner, like aspirin, coumadin, or plavix? Are you taking a NSAID for pain (like advil, ibuprofen, aleve, etc)? All the medication groups I just listed can cause bruising. If there is no medication causing this, perhaps you are taking some kind of herbal supplement (some vitamins) or eating something that is causing you to bruise?
I would let your health care provider know about your concerns if medications or diet are not one of the possibilities. There are also health conditions, like immune disorders or endocrinology issues that can also cause thin skin and bruising.