I would suggest you do look into it. She may be suffering from sibling jealousy. 
They have great therapists that can work through this. My daughter is bipolar and does the same things you describe. 
Do you have any mental illness history in your backgrounds? Suicide? alcoholism? depression? these are things they look for when diagnosing. 
 
If not then I would say she is probably learning some of the behaviors from the older girl. And also may have some anger about the new baby. You need to protect both children. 
If you do look into find a psychologist who specializes in childhood mental illness. 
 
A great website to ask questions if you think your child has bipolar is  
 
www.bpkids.org 
 
If you have any questions and would like to talk to me my name is Tammy 
 
email is mommaoof2@yahoo.com