Wow, something I'm an expert on. I suffered from eczema for many (more than 30) years and was hospitalised on a regular basis whenever I got what I called septic attacks as a child. Which sounds like what your young friend is having trouble with just now. Here are a few tips she might try.
1. No showers (they're too abrasive and make things worse)
2. No hot baths, try to keep them as cool as you can and don't hang about
3. Whatever cream or ointment the doctor has given her should be applied to a sterile dressing and not directly onto the skin. Again rubbing the area makes it worse and also, creams like Betnovate C are incredibly painful to use, putting it on the dressing rather than direct on the skin is less so
4. Keep the area cool, dry and covered as much as possible. Oh and if the dressings are sticking she can soak them off rather than pulling at the raw bits. If she's like me, she'll be very self-concious and want to hide under the thickest tights she can find. Don't! Nylon tights are bad as they hold the heat and irritate the skin, she might try cotton socks and leggings as an alternative
5. No hard (bar) soap, rubbing again. Use a Ph balanced liquid soap, the Simple range is quite good I find, but everyone is different
6. Drink loads and loads and loads and loads and loads of water, it helps to flush out the poisons
She also needs to get plenty of rest, put her feet up whenever possible and consider a vitamin supplement as she's obviously very run down.
PM me if I can be of any further help. I have loads of tips built up after years of practice.
Oh and antibiotics won't help much since the underlying cause of the eczema isn't an infection (that's the result not the cause), it's either stress, allergies or a compromised immune system - or a combination of these.