First off, please please please choose something other than a "special type of radiation" from an "unstable nuclear reactor prototype" that caused a "sympathetic detonation" of all nuclear power plants. I almost stopped reading after that point... then realized the whole point of this forum is to give useful feedback.
My guess is that your point isn't so much "radiation kills adults" as it is "nobody lives to be an adult," in which case I'd recommend having a bio-electrical nanobot accident that targets people whose is the perfect breeding ground but doesn't develop to the right maturity until a certain age.
One more note is that you say the internet still works but phones don't. Firstly, they run on nearly the same systems nowadays, so really that's not an issue. However, since the nuclear power plants died, many data centers are going to be offline (after their local backups fail). When those die, any other servers relying on them will start to stray and soon die. 998
Keep in mind that the internet isn't a thing you can set up and forget - it requires varying levels of maintenance by every individual organization on the internet. It WILL start failing fairly quickly. Not to mention that, when the adults died, they took with them the passwords to get into the various servers and server rooms to do maintenance.
But to get to your real question... In the near term, you'll have issues with procreation since young people are more at risk of having issues than people in their 20s. You'll also have the hormone-induced interpersonal drama without any adults to help temper it, so you'll likely quickly have factions form, some of which potentially going to war. It won't be until age 26 or so that the less-aggressive ones can start coming back together.
Since their bodies aren't aging, they'll need some way to distinguish their age (or, as they'll perceive it, their intelligence/seniority), which may be in the form of ranks or shirts with their age written on it.
In the end, though, society would revert to the old-west era of America until the adults' wisdom is recaptured. Except that they'd have a lot more technology that they don't understand and can't fix. 998