I would try to talk to the "girl in my chapter who is a nursing major". She will be able to tell you what her experience has been and this should help you. If you are unable to reach her or set a time for a friendly chat,
I'm sure that there are other nursing majors in other sororities...see if you can have a friendly chat with any of them and see if being a nursing major affected their time committments to their respective sororities. This should serve to help you make an informed decision.
When you write:
"I rarely saw her last year - she hardly came to our events, COBs, even meetings - because she was soooooo busy studying. Even other friends in other sororities claim that they are pretty inactive because of the amount of work that needs to be done", it's highly likely that that will be the situation for you as well, but only you can decide what works for you.
Let us know what you decide to do.