how bad will the burn be? herbal tea on 7m old

[PollyParanoia]

My friend was just round with her 7m dd and I made her a cup of herbal tea which was, we thought, out of her daughter's reach (she was sitting on her lap). But she lent right over and managed to spill it onto herself. We got her in a sink of cold water in about five seconds I think (the tea spilt on my friend so she reacted quickly) and the dd was wearing legging type trousers. After about 15 mins in cold running water we put cling film on and she went by taxi to a&e.
While I'm waiting for news can anyone give me any thoughts on how bad it's going to be? The water was recently boiled. The skin on her legs looked red, the colour it goes when they've been crying, but not at all raw and nothing that looked like it was going to blister. It's just that another friend's son was in A&E for a week with a similar accident and is still scarred. I feel so responsible (my house, I made the tea). I was also bloody useless in the crisis.
Polly

Bloody orange bloody broadband has been down so I haven't been able to update on this accident.
They went to burns unit the next day and everything is absolutely fine. She's very unlikely to scar and the burn hasn't affected the joint. They said it was all due to having got her to cold water very quickly as the tea could not have been hotter (no milk and just boiled). She has a couple of small blisters, interestingly on the leg which had less hot water poured on it, but had cold water on second. ie the cold water seems to be more critical than how hot the initial water even.
I didn't know that about cold towels rather than cling film. Nor that water should be tepid rather than cold (it wasn't particularly so in the case of our taps). In retrospect the towels would have been good for the journey to A&E. Also wish that I had called an ambulance instead of a taxi, but then I don't suppose it would have been much quicker and at least the wound had been properly cooled before the journey.
My friend is obviously a bit distraught still, but now feeling glad that at least it was a near miss situation as it turned out.
Everyone get a basic first aid primer and stick it on your fridge.
Thanks again for all these helpful messages. I was a total mess on Wednesday night. Friends certainly don't hold me responsible and very sweetly bought flowers to say thanks for the help.
Pol