U Haul Storage Lockout

The best course of action is to contact the individual who is on duty at the storage office.  Explain what has happened and ask permission to hire a locksmith so that you may gain entry into your storage unit.
A reputable locksmith will explain that they can do this work only with the permission of the storage office. 
You will probably also need to provide identification and if you can find documents that show you are the renter, that would help too.  

In addition to this authorization, the locksmith will only be able to perform their work during regular business hours.

So, after you contact the storage unit office and receive permission, you may contact a valid locksmith. 
When you do, it is helpful to know what kind of lock you have on the door. 
The most common types are disk padlock.
If you don’t know the name, give a description.

The other scenario common to storage units is that the lock itself is damaged and simply will not open.  In that case, you will again need the permission of the storage office to call a locksmith in order to have the unit opened.