I had bad acne when I was in high school (over a dozen years ago), and still occasionally break out, though nothing like it was back then. I had acne on my neck and back, like she did. I was put on oral tetracycline and had some dietary restrictions, though I’m not sure how much of an effect any of that had.
Does she wash her hair frequently enough? The oils from that might possibly be contributing to her acne where her hair touches her face and neck.
To keep my “adult acne” under control, I picked up the latest edition of Paula Begoun’s Don’t Go to the Cosmetics Counter Without Me. She’s been rating makeup and skin care for at least a decade, and has products analyzed to see if they can do what they claim. In there she outlined simple skin care regimens for different skin types. I use the combination skin one, but oily skin is probably similar - a simple version is something like twice daily washing with Cetaphil (a mild liquid soap that doesn’t clog pores - many bar soaps do), once or twice a day toner use (something as simple as hydrogen peroxide even), occasional use of milk of magnesia to remove excess oil (it has the active ingredient that those expensive clay masks do, and doesn’t clog pores), and nightly use of an effective AHA or salicylic acid (the latter penetrates blackheads better, I gather) to help keep pores from getting clogged up. Oh, and she recommends after washing, the occasional, gentle squeezing of any blackheads to try to unplug them. She warns to not overdo it to the point where you cause damage to the skin, or you’ve made a blackhead into a worse problem.
If you dry out your skin, you’ll force it to make more oil, and make the problem worse. This is probably why the product for very sensitive skin worked somewhat; most of those Stridex, etc., pads seem to have a lot of alcohol or other very drying, nasty stuff in them.
I’m not a doctor, it’s been a while since I’ve been treated for acne (or needed it), and I’m not a shill for Ms. Begoun, but I’ve checked through her books on and off for several years and she seems to know her stuff. Besides, her book is also a pretty comprehensive “Consumer Report”-type analysis of makeup and skin care products, and your daughter might enjoy looking through it for the scoop on whether those expensive cosmetics are really worth it (usually not), and what makeups really don’t clog pores so much, etc.