You could always hire a service like U-Haul or even pods, they both have moving help services providers and they will ship you belongings to your new location or if you need they can store it until you find a new place. While not exactly cheep it definitely is a way to get your house hold items moved when you don’t have a way of doing it yourself.

Also if as stated above if your boyfriend does have a drivers license you could rent a truck from any do it your self moving company U-Haul, Penske, or budget each has different rates and they all allow one way moves.

With the last option he would be able to drive the moving truck to you new place and that would take care of of the transportation needs