Transaction log backup
Shrinking is bad for performance and is a waste of time since it's just going to grow again. You need to add more disk space to accommodate the backups that you need. If you don't care about point-in-time recovery for the database, which it sounds like may be the case since there isn't enough storage even for a LOG backup, switch your recovery model to SIMPLE. With SIMPLE, you won't need LOG backups. But which recovery model you need is dependent upon your business needs of the database.