Chances are that your baby is gong to come down with a high fever after the doctors office is closed. You will then stay up half the night trying to get your baby to swallow some vile children's paracetamol. At least half of it will end up down their sleepsuit. Then you get to worry about how much ended up on the jumper and how much in the baby. If you give the baby more, you could overdose the poor child. If you don't give enough untold things will happen because you haven't reduced the fever.
In the morning, when you have gotten through all of that, the two of you head to the doctor. You are all bleary eyed and worried. Your baby is bright as a button. The doctor will tell you to keep giving the meds (and you still have no clue how) until the fever is gone and that your baby is fine. For a crazy moment you wish your baby would cry or something so you don't seem like a first class idiot.
In truth, the doctors will always say that they are always happy to see you when you are worried about your child. And even though they may see plenty of cases where they simply say keep doing what you are doing, they also get cases of more severe problems. With some illnesses like meningitis and urine infections you really need a doctor to diagnose and provide immediate medical care. In fact if you suspect meningitis you need to go to a hospital quite urgently. It is well worth having a family medical book. And keep the phone numbers for NHS Direct and out of hours medical care handy. I phone them a few times a year at least.
In the first year of my son's life he went through at least a bottle of children's meds, albeit some of it just landed down his pajamas. He had various fevers and teething pains, usually while his father was at work or out of town, etc!! It took another three years to get through the next bottle. Partly because as he got older he was better able to refuse the stuff!! Eventually they learn to tell you what is hurting them--which isn't as reassuring as it sounds! You still have no idea what to do if they have a pain in their side....or their jaw...or any of the other weird and wonderful things they come up with. But it all does get easier with experience.