"I get deeply emotional easily yet her emotionality seemed vibrant and frivolous yet not fully extroverted. I don't know. It got me wondering if I am not an Fe type"
Why would that suggest not being an Fe type?
An Fe leading type could view an SEI as being frivolous - they generally take emotions more seriously. That said, I wouldn't draw too much of a conclusion simply by finding differences between yourself and others who are supposedly of the same type.