Maybe "adolescent", then? Though I think that refers more to ages 13-20 or so. To some, I think young adult can mean 20-40, but to others it can mean 15-25ish, or at least that's what I think of when I hear "young adult". I don't think any of the english words like that have such a clearly defined age, but that could just be me. (Same with youth, which I think of as kind of 5ish-15, but aparently some thing of it as more what ungdomar are)
In my experience what age range an English speaker is talking about in situations like this depends a lot on the age of the speaker. 'Young people' can often mean anyone who's at least one generation younger than the speaker (though certainly not always).
It's one reason the term 'Millennial' is kinda loaded. It refers to a specific cohort of people, but kinda became synonymous with 'young adult'. So when people of that cohort began entering their 30s (and soon 40s), it started to feel really dissonant.
Here are some examples of how the word "youngster" is used:
"Advertising of the iPhone has led it to become very popular. If a youngster is going to get a phone for the first time, there is a huge change that he/she will get an iPhone just because it’s an option which everyone knows about."
"Promising West Brom youngster popular for all the right reasons. . . . West Bromwich Albion's most endearing midfield enforcer might need to toughen up, with Ben Foster suggesting the teenager is 'almost too nice.'"
"PEER GROUPS: Social skills --> youngster’s popularity during adolescence Some youngsters – both boys and girls –are both aggressive and popular at the same time"
"They're too quiet! What are those youngsters doing?" Parents, especially grandparents, would refer to youths who might get into mischief as "youngsters." It is a semi-affectionate term. Generally "youngsters" refers to adolescents, but the term can be used for a wider range of young people, including anyone younger than the speaker: "Those youngsters haven't discovered really good music yet."
I'm getting the sense here that 'ungdom' might be better translated as 'young adults' than 'youngsters' in modern English. It's clearly not (based on the comments) used in a way that would be equivalent to 'barn', but also obviously distinct from regular adults given the use of 'ung'.
It's relative - I actually just heard a woman in her ~60s call two people clearly in their 30s ungdomar, only an hour ago. She was obviously expecting a laugh, but still. But I'd say no younger than twelve, and without context no older than about 25. Something like that. Note that you might very well get a different answer from another native.
Sweden has a fairly wide range of dialects and sociolects, so getting different advice on pronunciation and idiomatics from different speakers is to be accepted. I generally aim to talk about the most general and common way of speaking, and note why if not.
It's not quite as bad as English, though. :)