No you cannot carry a firearm or concealed weapon on you into any post office since the Code of Federal Regulations prohibits any weapons whether concealed or not to be carried into a post office or on the grounds of a post office.
It states that no person while on Postal Property may carry firearms other deadly or dangerous weapons or explosives either openly or concealed or store the same on postal property except for official purposes.
That's what the Code of Federal Regulations states and is in Title 39.
If caught with weapons on Post Office grounds you could face imprisonment for 5 years or more.