IB full time advice

Hey, Guys, I am a rising senior graduating this December. I go to a Target school in the Midwest, and I am a non finance major. Summer Analyst recruiting was a bit difficult for me, while I had many super days, and interviews with BB and top boutique banks I ended up with nothing and got an internship at a small middle market boutique in Chicago. While I have an offer here for full time, and my coworkers area great and like me I want to work at other firms. My associate mentioned that everyone at the firm, has a lot of connections to other banks and they could help me. How exactly can I ask that without sounding like I don't want to work with them? My firm is small and I speak to my MD and Vp often. Here are more of my questions : How can I reach out for full-time opportunities and how can I find some? Which banks are hiring full-time analysts? How can I leverage my non finance major to get a full-time offer? I am learning so much in this position and I am given so many responsibilities. However often when I contact recruiting, they ignore me and I can't find many alumni at the banks I want to work with. Or often I get "we aren't looking for full-time" I have a 3.45 gpa, many finance extracurriculars. Sorry for the long post, just the clock is ticking, and I am a bit stressed ha.