The goal isn't to do everything. It's to pick what you say no to on purpose.
I got deliberate about time management and keeping track of tasks when I was a couple of years into my first academic job and feeling terrified about how much I had to do. It was clear my existing system of reading through emails looking for shit I hadn't yet done was not working. My email inbox was over 3,000 messages, and I was dropping balls left and right. Something had to give. I read David Allen's Getting Things Done and have used some version of his method for the last 15 years. I can't imagine surviving an academic job without it.
There's a million blog posts out there explaining how to use Allen's system, but if you're just starting, there are really only five changes you need to make to feel about 1,000 times better than you do right now. The main goal of this system is get stuff out of your head and captured somewhere, so you can free up brain space for actual thinking and living. If this list seems too overwhelming, just start with #1, because doing that alone will free you in ways you can't imagine before you try it.
Create a master list somewhere of everything you have to do, every goal you have, every call you need to return, literally EVERYTHING, which is separate from a daily or weekly to-do list. I don’t recommend using an email inbox or folder as a master list container for a lot of reasons (see #3). But you can use literally anything else. Apps like Todoist or Things, a notebook, a whiteboard in your office, a google doc. Whatever works for you. Why? Because conflating a daily or weekly to-do list with all possible tasks is confusing and demoralising. It feels like you’re supposed to do everything at once, and your priorities aren’t clear, so you have no sense of accomplishment. Once you start deliberately choosing tasks from your master list, you get a huge amount of power over your time.
List everything on your master list as either an action or a project (anything that requires two or more actions) rather than a concept. So not “boiler” but “decide whether to buy new boiler.” For projects, list out every action you need to complete them. My example here might include: “find warranty, read warranty, call repair guy for prices, research prices of new boiler, make decision.” Why? Because every time your brain reads “boiler” (or whatever other concept) it has to create that list of actions, decide where you are on it, and then find the next action. If you think this through once and write it down, then every time you return to the list, the thinking is already there. Plus you have the assurance that you won’t forget a step, because it’s all written down.
Do not use email as a to-do list or master list. Why? Oh my god, SO MANY REASONS. For one, you get distracted by incoming stuff constantly when you're in your email. For another, emails do not come in the form of actions or projects. So every time you want to do something you have to read the email and turn it into an action or project in your head. Tip: If you have a huge inbox, take everything not from the last week and archive it. Then assess the rest of the emails (and any incoming emails) to see if they require one or more actions from you. Create the action or project on your master list, then file the email in a new folder called "Action" for when you get to it.
Routinely triage your master list and assign actions from it to your day or week. How often you do this is up to you, your job, your deadlines, the urgency of stuff that often gets assigned to you, etc. But it's important to BE REALISTIC about how much time things take as you assign your actions to days or weeks. Don't overload yourself. Again, it's demoralising and your priorities aren't clear.
Routinely review all the places that tasks come to you and add them to your master list. I recommend at least once a week for this, but again, it's going to depend a lot on you and how your job/life works.
As you start to try this out, remind yourself that goal isn’t to do everything or fill your schedule. This is what I call the time management fantasy, and it is especially pernicious for women. The way out is to accept that you are always going to be saying NO to something, so the goal is to pick your NOs on purpose. When you capture everything into a master list your review, you give yourself the time and mental space to see what you actually want your priorities to be. This can be anxiety provoking, so it's useful to remember that the anxiety will come up either way--whether you actually know for certain what's on your plate, or just have a vague sense that it's way too much. If you use this approach, though, you can actually move past the anxiety, because you'll have given yourself the time and space to identify what is most important to you and actually do it.