Keep looking. You may be able to find an owner that knows their renters are not going to be returning next year. If they have underclassmen in place as renters now they may be waiting to see if they will be returning for next year's classes.
As the owners become aware, things will open up. Don't panic...but continue to search
My advice is: If you are going to rent near your school, the landlords are aware of when you can move in. So dont be afraid to tell them your situation and ask them if they will hold the place for you until June with a one or 2 months deposit.