I'm not sure if this can work for you, because I don't know your boss or work culture, but can you ask for help? And see if someone else could take a couple off your plate? When I was in the deepest depth of my burnout, I finally had a talk with my director and laid out all of the tasks that needed to be accomplished and how long they were going to take. That helped me because it got the weight of it all off my shoulders and we were able to get some of the tasks canceled or handed off to someone else. Your ego will HATE that, but you are in charge, not your ego.

Also, do you have a single list of all of your tasks? If you are keeping it all in your mind, then your mind starts to feel cramped, which can make it worse. I find a brain dump of everything on my plate helps a lot. Getting it all out of your head and into a list will help get you started. Then prioritize the tasks. Before leaving work each day, review the list to see if the priorities are the same and create a todo list for the next work day of 2-3 tasks. When you get to work, only focus on those, if you can. If you don't prioritize then everything seems to be important. As you get each task completed, cross it off and give yourself a mini reward. Maybe take a short walk or just get outside. Drink some water. Give yourself a small pat on the back for getting that task done. Go you. If you get done with those tasks early and you can, pick the next most important. If you don't get them all done, recognize that you're trying your best and then let go. I know your ego doesn't want you to, but leave work at work. You are not your work. If you over identify with your work self, eventually that's all you are.

Again, good luck. It's good that you recognize the problem.

Edit: Sorry that all sounds like trying to fix the issue rather than listen and sympathize. I do recognize a lot of me in what you've written.