Yes, what you ask for is impossible, it's like wanting to take a swim but not wanting to get wet I'd say. You can get one, but not the other.
If you wanna blast away in the car or being in a dense crowd and still hear the phone, there is always the option to fire away a square-tone at full blast in the vicinity around 1 to 3 KHz. But at least in the crowd there's a good chance the ones around you will hate you. Immensely. That's where the human hearing peaks, and also the range infants like to scram in. You can tweak the tone to just barely break through the music and/or crowd, but playing at school...I'm not joking when I say this: Make sure that noone around you have issues with aggression, because this WILL piss people off to a degree you can not imagine. It's EXTREMELY painful to hear at the level we're talking here for some people, especially people with between mild to and heavier hyperacusis, and really really annoying for most other.
At school, on the other hand, there are neither no need nor desire for breaking through anything, so here we need a very different approach. Here, pink noise is technically speaking a very good choice, but it can also be a wee bit too anonymous if you're unlucky. The keyword here is having an as flat and wide a range as possible, and if you make a ringtone from a song, it's not a bad idea to lower the rage between 1-3 KHz somewhat to make it less distracting. Most phones don't go below like 250-300Hz, but lower frequencies are good for keeping thing softer, so raising the lower end is also a good idea. It might get a bit muddier as you can't reach the really good stuff, but it will also be less distracting. Just don't overdo it.
My sincere advice to you regarding this is: Go with the soft option, and buy an external more powerful vibrator instead. There's a wide selection I've seen over the years, and one of the easiest ones I've seen so far was a wireless one that just plain reacted to closely nearby signals. I had mine around the neck. I've also seen several that can be connected directly to the phone and are run by battery.