I would call your pediatrician and ask him/her. It's important for your ped to know what's going on and be able to ask you questions and make sure that what you are seeing is all within the scope of "normal."
That being said, a steroid shot is, I believe, adrenaline to get something out of your child's system. Giving your child adrenaline is most likely going to cause their hear to race and them to feel agitated. So I suspect this is actually quite normal, and it will just take your daughter some time for her system to be back to normal.
But please do call your ped, just to be safe. You would hate to take my completely unprofessional advice and not address an important health question with your doctor.
ETA - Our son was 3 or 4 months old when he received a steroid shot. It was for croup. Just saying, there really are reason for a 4 month old to get a steroid shot.
He's 11 now, so those few days are very fuzzy for me. But I do remember he was not a happy camper for a couple of days at least.