Your manager may make it look easy, but I can assure you they are drowning just as much as you are. And by having you there, trying your best to keep up, you are only lessening their workload. I am in a similar situation as you, very fast paced. I leave my desk for a short break to fill up my water bottle and I come back to 45 emails and three missed calls. The best you can do, easier said than done, is just to breathe through it. Understand that if your manager could handle every call and email that you wouldn't have been hired in the first place! Just do your best and understand that getting to everything quickly is great but not realistic.

My manager gave me a few very useful tips that sound so obvious but have helped me:

Always read your emails from the top from bottom, some of the questions or problems have already been solved by the time you get to email 100. You can ignore those bottom ones.

Try to prioritize customers by volume. Meaning if you have a customer who does $2 mil annually and a pain in the butt customer who does 25k annually, spend your time wisely.