Why did she choose 姐姐?
She identify herself as 姐姐 to show she is “powerful” or “knowledgeable” in doing whatever you don’t know how to do. Sometimes you call a female 姐姐 for showing respect. Even for people younger than you, they may still identify themselves as 姐姐, because 妹妹 is too flirtatious. However, I don’t think it’s a good idea for you to call a female 姐姐 when you know she’s clearly younger than you (not in your situation, as she has called herself 姐姐). And, females don’t like to be called 阿姨 by strangers even though they’re much older than you, so 姐姐 is a safer bet. 

Another popular term to call young females (even though they might be younger than you) is 小姐姐, which has a lot meanings than it used to be. So the use of it depends on context, but generally I treat it as a nickname for young beautiful females. Pls be careful using it though. A lot of materials online you can search about.