Reactions to steroid injections have been reported and can be either local or systemic. Local reactions refer to skin and muscular changes around the site of the injection. Rash, redness, tenderness, and as you described, skin peeling can occur. Muscle spasms present at the time of the injection may go away (a positive side effect of the drug).
Systemic reactions are more along the lines of facial and/or whole body flushing, elevated blood pressure, nausea, and more rarely, vomiting. These responses occur because although the steroid is injected into a local area of tendon or joint, the blood system does absorb some of the drug. The active ingredient in the drug can then circulate throughout the body resulting in more body-wide reactions.
Any of these reactions are possible but not typical. Even though they are not uncommon, the physician administering the injection should be informed of any adverse events. This information should be placed in your permanent medical record. You may still be a good candidate for future steroid injections but the history of a reaction dictates careful observation and follow-up.