Most first time parents due to inexperience, panic in the face of medical emergencies. Me and my wife for example have two totally different approaches to emergencies such as the frequent bumps and scratches that sends your child running to you so learning to recognize something serious is the key and experience would educate you best. My wife gets into a panicked state every time she sees blood accompanied by the uncontrollable cries of our child, I merely step back, take a look at the situation and analyze the situation if it needs medical attention or if first aid can do the trick. For example, an open wound and compound fracture is always serious so speed to the hospital for care. High fever during teething is normal and can be handled with analgesics while being in constant contact with your pediatrician who would tell you to get help if needed.
Having experienced medical emergencies as a volunteer which developed my abilities to recognize life-threatening and trivial injuries, just hope more people would recognize this as a vital skill to have for it helps you lower your insurance premiums. Do some research on the web for health tips that can add to your knowledge of which emergencies to treat seriously and which are mere casual. Information and knowledge is the key, the more trips you take to the ER, the more a risk you are for the insurance firm so they have the option to ask more for insurance.