I agree with what everybody said. I was a NM this year, and it was tough for me to make my Big list. I didn't really want a senior to be my Big because I wanted to have someone to develop a relationship with for as long as possible. My cousin happens to be a senior, and I put her on my list, but a few down. The majority of our chapter ended up with a Little.
I ended up with my first choice (and I was hers), and I adore her. She's a sophomore, so I know we'll have lots of time to bond, especially when I move into the house next year. I'm her first and only Little, which is kind of fun.
Boy does she spoil me.
But you don't have to be a Big to be close to a new girl. I'm close with a lot of the other girls in the chapter. I'd say get to know the NMs, hang out with them and stuff, but give someone else the chance to take a Little, unless you have to.
I bet one reason your Little doesn't want you to take another one is because she's New Member Educator. She's probably pretty close to the girls, and doesn't want any of them to end up Big-less so quickly.