Should I Be Concerned For Body Injuries After Slipping?

At 3:00 pm today. I slipped and fell, landing on frozen black top. I fell primarily on my right side, striking my posterior, lower and upper back, and the back of my head. As I currently have a cold, I cannot state whether or not I'm dizzy or unsteady as those were symptoms that were present at the time of injury. I do not have a headache nor am I nauseous or vomiting, but as I have an infant, I am doubly cautious when my health is concerned. Should I seek medical assistance, specifically that of requesting a CT scan? Thank you.