I’m a ‘floaty’ person too and I have found that a subtle ‘awareness chime’ helps a lot. Just a subtle alarm that I have programmed to go off every 20 minutes. I told some co-workers that it was a reminder to drink more water, but in reality whenever I hear the beeps/or feel the vibrations I ask myself if I’m doing what I’m supposed to be doing (according to my schedule, priorities, deadlines etc.) and If I’m not, why not. It helps me keep track of the flow of time and how I’m spending my hours. Perhaps this can help to get more of a grip on your current workload while you’re figuring out whether or not you want to keep at your job or not and pursue a diagnosis.
And if you are like me: Always write sh*t down. When I’m asked to do x during a meeting I will forget it as soon as the meeting is over. If you commit to something or are supposed to do something write it down asap. You can also send them an e-mail confirming what it is you are going to do for them. It takes work to get trust back if people think you’re unreliable etc, but it is worth it to try extra hard to fix this if you decide to stay in your current job.
Also reading your post I wondered what you wanted. Do you want to get ahead? Do you feel you have to? Is your company promoting people based on seniority or whether or not they would be a good teamleader? Will they let you go once you hit a certain number of years without being ready for the next level? Could you be satisfied not getting to the ‘top’?
I think that when you are able to understand yourself a bit better and to manage yourself a bit better you will find that many techniques that help you stay on top of things are also usable to manage larger projects and more people. I’m rooting for you!