Another option also involves buying something. Historically, bakeries have used something called extenders or cake frames of various heights to place on a sheet pan. They form the walls for the cake, i.e. the sides, and are still used by many bakeries today. Hence, the term “sheet cake.” But if you can’t find a place to buy a proper cake pan, doubt you’ll find a cake frame.
Have you checked around thoroughly in your locality? My cake supply store not only sells but rents pans of all shapes and sizes.
Another option. You don’t say what size sheet cake you need to make. A full sheet? If you have a 9x13 cake pan, that’s a quarter-sheet size in bakers’ terms. Bake your cake four times and slot them together on an appropriately sized cake board. Ice them as one cake. No one will know the difference, especially if you slice it where the cakes adjoin each other.
Last resort, look at the disposable type pans in your supermarket. Have never tried to bake a cake in aluminum foil. Anybody else? It might work.