Change my physical address on my wireless account

I have tried to change my physical address on my phone and on a desk top with no luck it says there is an error message... So I call and of course they say... if I moved they will do a move of address change that can take up to 24 hours to process. Crazy for sure. The only service I have is wireless and I am trying to order a new phone online but it will only let me send it to my old address.  Also the person I spoke to at ATT was useless as usual. Was more interested in getting me off the phone than actually taking ownership of yhe problem within their system. What do I do?