I just bought more storage for my iPhone and it still is refusing to back up due to lack of space

You cannot buy more storage for your phone. It will always have the amount of storage it came with. You have bought space in iCloud, Appe's syncing service. To create more sace on phone, you must delete photos, messages, apps, etc.. Be sure to save important photos and data to your computer or an external drive. Check these links...

How to check the storage on your iPhone, iPad, and iPod touch - Apple Support

Clear Other storage on your iPhone or iPad - Apple Support