Every account manager I have managed has had a task list. The ones who never seem to be drowning have something different: a list of commitments they have made to other people, tracked separately from the things they would like to get done for themselves.
Two different lists
A personal to do list is negotiable. If you do not get to updating your notes today, the only person affected is you. A commitment is not negotiable in the same way. If you told a customer you would send pricing by Friday, or told your manager you would have the QBR deck ready before the call, someone else is now planning around your word.
Treat these as two separate lists. Commitments get reviewed daily, without exception. Personal tasks get reviewed when there is time.
Write down the promise the moment you make it
The single biggest cause of dropped commitments is not disorganization. It is trusting memory in the middle of a call where five other things are being discussed. The account managers who never drop a ball write the commitment down the second they hear themselves say it, before the call even ends.
If you catch yourself saying "I will get that over to you," stop and write it down before you move to the next sentence.
Rank by who is waiting, not by what feels urgent
An inbox alert feels urgent. A customer who has been quietly waiting three days for an answer is actually urgent, and does not always announce itself. At the start of each day, before anything else, scan the commitments list for the oldest unresolved item and handle that one first, even if it is not the loudest thing in your inbox.
Fifteen years in, the account managers who get promoted are rarely the ones with the most sophisticated system. They are the ones whose word is reliable, because they built a habit around never letting a promise slip through a gap in their memory.