You need to fill out a FAFSA as soon as possible. The process is painless and everything is electronic. Within a few days, the school will have the information and you will be able to proceed with an application for the student loans. With a high EFC, you just won’t be able to get any unsubsidized loans. I don’t think the banks look at a declared major, but what they really prefer is a Title IV school (no trade schools, etc). I’m unsure how long the “verification” process takes for the banks, but just call the financial aid office to understand the process flow for that school.
I would try to secure funding as soon as possible as there have been a number of lenders in the FFEL program who are not offering loans as the government subsidies have decreased, lowering the overall value (in addition to the fact that there are no capital markets for SL paper right now). If the school uses the Federal Direct loan program, you should be fine.