To answer the original question- yes! I think a disorganised person can become more organised!
It does take practise, and of course learning how to do things differently.
But the key to change is you WANT to change.
I was very like you and I have adopted lots of little tips from training courses, and have become ultra organised at work. I now think that actually I have dyscalculia and all my systems I've put in place really help me overcome this. Here goes with my techniques-
List. You need a to do list. One it's nice to see everything ticked off. Two if it's humongous then clearly you have to schedule in time to get through it. Three you can show it to your boss and say- this is my to do list how would you like me to prioritise it. Do this for a few weeks until you get to know what your boss wants done first.
Look at your list and decide where the tasks fall in this matrix- quick/ long time to do vs difficult/ easy to do.
So decide when you can get the quick easy tasks done. Plan in the quick hard tasks, quick difficult tasks. And make a start on the long difficult tasks. And so chunk these down so you can put in your diary when you will work on them.
Which leads to the diary- outlook is marvellous for adding in reminders, to do list items. Yes you need to keep it up to date. But 20 mins per week updating it is worth it.
Plus outlook can be COLOUR CODED. no one else I've worked with ever uses this. But it's great. You can see at a glance- meetings, project work etc. (I put difficult stuff in red, lunch in grey, 121s in yellow, team meetings in green) and yes it would beep at me to remember to stop for lunch (I often forget).
Work folders- use slip folders & write on them using a sharpie ie 121 project x etc. then you just pick up the right folder, blank paper & a pen and you are good to go.
I even colour coded the blank paper I used to take my meeting notes on, as it helped me remember stuff. But that might be a bit extreme!
One last tip- Microsoft OneNote. Wow this is an AMAZING product. Evernote etc doesn't come close. 60 quid to buy the full version, it's recently gone free on the web as a cut down version. So you can try it at home to see if you get on with it.
You can clip web pages in, hyperlinks, and screen grabs.
Also anything you type is searchable, and it's super easy to add tags.
These 2 things mean it's v quick to recover info you need to know/ remember if you have a rubbish memory & you can bring your laptop into meetings.
Again you can colour code the pages to match outlook, to do list items sync in outlook. You can put emails (as a wee icon of an envelope) into the notes. It really is marvellous & very underused software. But perfect for the disorganised person striving for organisation.
Ok so that's a lot of info. But honestly I work like that and I don't miss stuff my boss is happy & I'm so much less stressed.
Hope some of those tips helps you!