Get used to never catching up. There's always something somewhere that needs attending. IT workers are familiar with this predicament. We call it 'technical debt'. How can we prioritize when we are faced with overwhelming demands? It's simple. Prioritize issues with severe business pain and high urgency. I use the model below for guidance:
Address issues occurring in quadrant 1&2 first. In IT it's usually obvious where issues fall e.g. the phone system is down, the custom facing application has poor user experience, the database is corrupt, etc. When ambiguous situations arise and priorities start to blur then consulting with clients, the boss, and stakeholders becomes critical. Literately ask them , "What is important to you?". If they can't answer it might indicate a non-critical issue or it might indicate you're talking to the wrong person.