HELP! Do I have to wait until fall recruiting season?

I have a BS and MS in a quant engineering field from a target school, just graduated from my MS program. I'm trying to get into traditional banking. I had two finance internships, my current one is with a FoHF. I've been applying a lot and have had interviews but still not landing any FT offers and the postings seemed to have slowed. Should I continue to work my internship and wait until fall recruiting season? Will they accept FT applicants if you are not a senior or in your final year of study?