I was on antibiotics long term for a dermatological condition (not HS) and while not ideal boy did it beat the pain and suffering from the condition itself.
I just Googled HS and there was a laundry list of solutions from antibiotics to bleach baths (only if approved by your dermatologist) to biotic treatments, injections and/or surgery, laser treatments...the list just went on and on...so it seems like there are a lot of treatments to choose from that your dermatologist can choose from or help you choose from to help your daughter.
First off for home treatment I would suggest a healthy diet with no processed sugar...none at all...sugar feeds all sorts of bad bugs from bacteria to fungus etc etc....cutting all processed sugars out for say 6 weeks to see if it is helping and then looking into cutting out dairy as well could really be a game changer as far as her break outs go...
I would also consider a long term treatment of antibiotics because if they can get it under control then you can keep it under control with diet and other lifestyle changes. (While she is on the antibiotics make sure she is on a really really good probiotic to help her gut biome stay healthy and eat plenty of fermented foods, sauerkraut, kimchi, kombucha, fermented lemonade, etc etc).
The biggest lifestyle change is always your diet as we are what we eat...and if she is overweight which one of the articles I read said is a contributing factor to the condition helping her clean up her eating will help her lose weight and in turn help stop the breakouts.
Good luck!!