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Clarification: you have a finance major and some finance experience as well as some event planning experience, but you want to become an event planner.

Event planning is not an industry that recruits. You need to aggressively seek out these positions. My best advice is to get an event planning internship, and to join a professional organization dedicated to this industry. They will have student discount. Attend as many networking events as possible. Talk to professors at your school who teach communication classes. They will be able to send you to talk to people in the field about event planning. Take these as informational interviews.

Most event planners won't hire you if you haven't had some kind of event experience-- be it planning events for a sorority, university event, an internship, etc. The pay isn't great, the hours are long. It can be very rewarding and the ideal candidate has an eye for detail, is calm and level-headed, and isn't afraid to get a little dirty and do some heavy lifting. In the beginning, you will be doing more onsite tactical implementation than you will be actual strategizing the event.

Choose where you want to go after graduation and target your resumes to that location. From personal experience, you have a better chance at being hired AFTER you've relocated-- employers feel more confident taking a chance on someone who lives near them. (This doesn't necessarily apply to companies and industries that do heavy recruiting and consulting). Instead of sending a blanket cover letter, tailor your resume and letter to EACH job. It will take longer, and you may send out less queries, but you will get a better response. Good luck.