A harmful side effect would be breaking out in hives. Yes, having chills is detrimental to your sleep, but not dangerous. Hives are a sign of anaphylactic shock, something that can kill. If you break out in hives from a medication, you should call an Urgent Care. If you get hives and labored breathing you should call an emergency room.
You could either have Tonsillitis or something else, worse or not. Tonsillitis is usually caused by a viral infection but can be from a bacterial infection.