I would start by requesting your medical records from the birth. The hospital will have a medical records department, and there might be a small fee.
That way, when you make an appointment with your doctor, he or she will be able to see exactly how the IV was placed, if there were any complications (like if they had to attempt placing the IV three times before it was successful), and exactly what medication was in the IV solution.
The doctor may have a reassuring answer for you, or refer you to a specialist, but at least you'll be able to be informed.