Do self-storage units have to notify you if your fees change?

That depends, but in principle, yes.

The 'depends' part is because when you signed the storage contract you would have implicitly or explicitly agreed to the Terms and Conditions offered by the self storage company. Those Ts and Cs may or may not say that the company will inform you of any change, perhaps a certain number of days in advance.

The 'in principle, yes' part is that it is good practice for any company to inform its customers of any changes in their charges in advance of sending out the invoice or taking the direct debit. In some jurisdictions, consumer protection laws will make such items mandatory, even if you have signed a contract which does not require prior notice.

Even without the legalese, I would go to the company director or manager and raise the issue directly but politely, and if they do not see your reasonable point of view, I would move to another company. In my self storage company