picking at its neck

Question
I just got 2 zebra finches, one of them died unexpectedly during the night. They were about 5 weeks old when I got them. Now the one that is left (I think it may be a girl) is picking at it's neck. What should I do? I covered it's cage to help it relax, and I have been giving it fresh water everyday. Please help, I love my little bird.

Answer
First of all, I am sorry about the death of the male.
This brings me to my first question, do you have a heat lamp on them? Finches need a higher temperature than we do and so a heat lamp keeps them healthy.
I think she is stressed but I can't be certain.
Does she sit on the cage floor?
Are her feathers constantly puffed out?
Is her breastbone sticking out like a knife?
Is she sleeping during the day?
Is she staying near the food dish?
Is more food ending up all around her instead of in her?

Even if you answer no to all these questions, take her to an experienced bird vet (if the guy prescribed Rice Water or something like that, find a new one. That one is obviously an idiot.