Bruhhhhh, why did you buy a 338 lapua mag if you can't afford to reload for it?
I'll try not to be the asshole who gives no solutions so heres your options:
Get with a company like Unknown Munitions(there are others I believe too). They make custom loaded ammo, and you CAN send them your brass, but obviously cannot send them anything else in the process....besides bullets.
GOOD custom ammo like that is NOT cheap. Then add in that skunk factor that is 338LM and that shit starts smelling like $100 bills real quick.
I would hit up Unknown Munitions and see what they'd charge. IF anyone, I would imagine they can make you legit ass ammo with your brass for a reasonable price....which is still not cheap but for what you're getting, its legit.
Then compare that with the cost of buying a bare bones loading setup to make accurate ammo....of course then theres that whole experience factor. The less experienced you are reloading the greater chance you have of making ammo that isn't up to snuff....but it can be done. Lucky for you Large Rifle Magnum primers are still in stock at some places and you can probably find a useable powder somewhere.
I think those are your only two real options....short of finding factory ammo that works well in your gun lol