
if he missed school and didn't get better the next day i think it's enough to go to a hospital. when you're weak and dizzy like that you can't be alone. in my country you go to the emergency room and you can either get shots and go home or get admitted to the hospital depending on the doc's decision and/or diagnosis. it also depends on your luck, you can get a shitty doc who'll prescript you some random medicine and let you go or a good one who really cares about your state.

Firstly, I did start of by saying that fevers and colds CAN actually get serious. You can get a fever from a lot of things with a more severe underlying cause, such as an infection, for example. And if it's really bad, a hospital may want to keep check on your vitals overnight.
However, colds are rarely that bad, and if they're bad, they're usually on the verge of something else, such as pneumonia or sinusitis. And in these cases, there are some measures to be had. You can't cure a virus (yet), though, and thus there are at most treatments to ease the symptoms of colds.
Also, hospitals will of course not want a cold epidemic to spread, and prefers to let you rest at home.
My main point is, though, that it's an overused plot device. And it's not used all the way, because authors rarely want to keep the characters bedridden for too long. It takes away from the seriousness of it all when they're fine the day after. I swear, I've seen this happen countless of times in countless of series (not to mention the "Oh, no, don't sleep on the sofa, you'll catch a cold!".....)
I know fevers and colds can actually get serious, but isn't it becoming way overused? I mean, I don't know how the hospital system works over there, but it's gotta be pretty lax to give a bed to someone with a cold. Around here you'd get sent home very soon if you came in for something small like that.
It's usually only used as a cheap plot device for small progression, as well.
Of course you can get sick, but that same plot would at the same time not allow the characters to be bed-ridden for a couple of weeks. They're usually up and about the next day, as if nothing happened. It feels shallow.