I think it's just something you get used to - how old are your kids, and had you been around other kids a lot before you had them?
I tend to judge mostly on their behaviour - if they're not doing their usual activities, not eating as much as they normally would, far more tired than usual, etc. In one of my group chats we call it the KitKat test - if you offer them a KitKat and they say no, they're ill 😆 (named so because the first one to do it used a KitKat, but test can be executed with anything that would apply to your kid!)
There are also several things you have to run through in your head when they say they don't feel well/tummy hurts etc - have they drunk enough today, are they hungry, are they tired, have they eaten too much crap, have they been doing something that's made them dizzy/sick, are they anxious about something, do they need the toilet. If a drink of water or a sleep or a big poo will sort them out, probably not deathly ill!
Obviously the above is just the day to day stuff - if things clearly get worse then I do keep an eye on temperature and urine output. And keep Calpol in the house at all times - magic stuff for temps. Ditto ice lollies - if you can't get them to drink, you can sometimes get them to have an ice lolly.
I think also it might help to learn the signs that would make you instantly call 111 - e.g. blood in pee, blue lips, grey skin, sudden loss of balance, no pee for more than 12 hours, face drooping etc - not to panic you but as a reassurance that it's not any of them iyswim?