From the noun fangirl
V. To make loud high pitched noises (this includes squealing, yelling, or talking so quickly that it doesn’t sound like they are actual speaking a real language) or show their excitement for the object of their obsession though movement (this includes jumping glomping, running in circles, etc.). Fangirling involves a lot of physical action unlike fanboying and can be quite annoying.
One does not have to be a girl to start fangirling though most girls do.
Also see fanboy