How are my chances for BB I-bank recruiting this fall?

So I'm going to be a junior at University of Miami this fall with a 3.8 gpa and two prior internships.

I just finished an Asset Management internship at a BB in New York City in their Alternative Investments group last week and summer before I worked in a family business (not finance related, but I still developed an idea of the business world etc...)

I have good E.Cs, and know a good deal of technical information even though I'm not a finance or accounting major(DCF, APV, WACC, basic financial statements....)

I have people at the BB that I was at this summer that are willing to help me out and write me recommendations in order to help me get into the IBD at that BB.

I have tried contacting some Wall St. alumni from my school, but, quite frankly there aren't many on the Street.

I just wanted to know if I have a fighting chance or if its a long-shot and I'm better off pursuing a couple other industries that I'm also very interested in.