Do I have any chance at an IB Internship?

So basically, I am looking to go into a career in investment banking. I'm really late into the planning and haven't had much guidance. I have been in a non-target school for my first two years of college, and basically wasn't even sure of my future- I was completely torn between a few different paths.

Last semester, I decided on an IB path- and while I knew it'll be hard, I am starting to think it's impossible. I will be transferring to a semi-target/target school next semester. I worked my ass off and still have a perfect 4.0 GPA. I have a variety of volunteer experiences (I know it won't matter, but can't hurt for my character).

However, I don't have any internship experience in Finance. After reading forums, talking to people etc, I've come to the impression that it's nearly impossible to get a good junior year IB internship without related internships. At this point, I just don't know what to do. I'm not sure if there are any other internships easier to get into with a path to IB- but any advice? Anyone have a similar experience?

Anything is appreciated.