There are several master wholesalers that sell authorized items to resellers such as us. Contact the NFL, NBA, etc directly and ask for their marketing dept, and they can usually direct you to their master wholesalers. It make take a few phone calls & "bird dogging" to get the sources you need, you just keep trying.
If you're looking to actually produce the shirts yourself, that's much more difficult to get into, as you'll have to be licensed, sign contracts, have a business that been around for a long time, provide all types of financial info, be investigated by theassociations, have your facility inspected, pay royaltities, keep really good records, etc. They only award these licenses to usually really well established printers.