Why am I more sore 2 days after my car accident than I was on the day of the accident?

Like working out. It is similar to when you work out. You do not feel it until the next day.
Missed injury. Pay attention to new areas of discomfort. Very often, the trauma team or emergency medicine team are focused on immediate threat to life an limb. It is always possible there is a missed injury. This is not necessarily poor care, but a result of the complexity of dealing with multiple blunt for trauma. If in doubt, you may wish to seek additional medical care. Usually missed injuries are small.
Trauma pain. Our muscles spasm during trauma as our reflexes try to protect us. Inflammatory reaction after musculoskeletal trauma may peak after 72 hours. Check with your physician. Even "mild" trauma will cause chronic pain if ignored.