Typically when you purchase relics off the Relics page, they open immediately and will be in your collection, even if the game crashes for some reason. If you haven't already, be sure to check your collection for any new fighters, sorting by 'recent' will help with that.
If you're still unsure about the status of your Relics, I recommend reaching out to our customer service team and they can investigate. Please go to skullgirlsmobile.com/contact