God what a nightmare. She might be in a sort of denial about her condition. You know how it feels to be a teenage girl. It's not easy at the best of times. But to then have a chronic skin condition thrown into the mix? I expect she has been teased about it more than once while growing up. People - especially youngsters - can be horrible cruel little bastards.
Perhaps there's a bit of "if I ignore it, it will go away", or blocking it out rather than dealing with it.
Emollients are not particularly pleasant to use. They feel greasy and it gets on your clothes (and doesn't come out in the wash). Oilatum in the bath does help, but again, it's greasy. (Can't get it in your hair, etc.)
It's really important that she embraces it and starts to treat it properly. You said she "won't allow you near it". And it may be that you have transferred some of your worry about it to her, so your stressing about her eczema makes the whole thing worse for her.
I really feel for you. Here are a couple of suggestions:
Speak to your local pharmacist about the problem and see if there are any creams they can suggest that might seem more appealing to a teenage girl. If they find something, do NOT say that it came from you. Say something like a colleague at work also has the same thing and gave you this to pass on to her.
Have a look online for teenage support groups for eczema - you will find lots of information about how this affects young people and their self-esteem.
Do not speak to your daughter about eczema unless she brings it up first. (Unless she's having a bad outbreak and needs medical attention.)
If you don't already know - find out if it is allergy driven and eliminate as many allergens as you can from your home.
Look up celebrities with eczema (e.g. Kim Kardashian has psoraisis and has spoken about it, and some of her snaps show patches). This is handy to know just in case you get a chance to mention that oh, so-and-so has that.
Good luck. Eczema is a real bugger but it can be managed and sometimes it just clears up and goes away, although that can take a long time.