I agree it looks horrible if you’re unfamiliar with burns but that’s completely normal. The green tinge is nothing to worry about yet, that’s just pus drainage. It does denote a minor, superficial infection but if she’s feeling otherwise fine that can be cured at home very easily.
First of all with proper care it will scab over/start to dry up in a few days. In the meantime keep it uncovered and clean with plain, cold water a couple of times a day. If she can stand it soak the finger once or twice a day in salt water too. Boil a litre of water and dissolve four teaspoons of table salt in it. Once it’s cooled either soak the finger in it or soak sterile gauze in the water and apply to the burn. Whichever method you choose she wants to do that for about 15mins once or twice a day for about two or three days. The salt treatment will dry it out and make it look drier and “scabbier” rather than wet and puss-shiny.
Once it scabs over/ looks drier in those two or three days and no longer has that greenish tinge it’s worth getting a pack of Hydrogel Burn Plasters like these ones for the daytime. It will promote healing and keep it covered so she doesn’t knock it and agitate it as it’s on such a prominent place. At night take the plaster off and use just some normal Savlon or Sudacreme on it (other brands are available!) or a gel like this one Savlon one. It will help with healing and keeping it from getting infected.
You should see your GP if the wound becomes smelly or very/more painful or she develops a fever (over 38 degrees). You should also see the GP if it’s showing no sign of drying up or healing after 14 days from when she did it.
I’m not medically trained but my husband sustained a nasty third degree burn last year and had to go to A&E with it. The doctor explained burns generally to us and gave us some really useful fact sheets (where most of that info above came from!) then later in the year I gave myself a nasty burn in a similar spot to your daughters with a hot glue gun. I followed the advice above (with a similarly green-tinged wound) and it healed very well with minimal scarring there now.
Good luck to your daughter, I hope it feels better soon.