Going through charector creation, and booming blade doesn't show up as an option for warlock spells, it shows up for sorcerer, and the spell says it belongs in both class lists, any one know how to get the spell to display for warlocks?

Hello Polaris_, the Booming Blade cantrip is from the Sword Coast Adventurer's Guide. Is there a chance that your Sorcerer character is presently in a campaign that has sharing turned on, which may be giving you access to books you may not otherwise have, while your Warlock character is not in that campaign?

So looking back through it, sharing is turned on for the warlock, and the dm has booming blade, when the gm tests it on sorcerer, it shows up, when the dm tests it on warlock, it does not show up, when I test it with either warlock or sorcerer, it does not show up, so it's a bit odd

Maybe suggest he toggle content sharing off then turn it on again.