I think you can. I'm also a teacher, naturally disorganised but my pupils all think I'm the most organised person in the work. My thing is colour coding. I have a colour for each class, they get a small sticker at the top of their books with their class colour, I write my plans up in that colour, any homework handed in goes into a tray with the coloured label.
Also, lists. Instead of a daily to-do list, I have a rolling to do list. Urgent stuff gets written in red, everything else in black. I always try and clear my list by Friday, but some big things do roll over. I rewrite whatever hasn't been done by Friday onto a new one for Monday morning.
I also have a weekly countdown which I write in every "Monday" any deadlines I have thatmonth - I do this at the start of the year or as I find out about it. So I will will write "s1 reports - 4 weeks" then the due date in brackets. If there is a big clash, like two big things due in the same week, I highlight them too so I can see and plan for it.
I also set aside time each week for particular tasks. Its quite easy as I'm a teacher so I know where my free periods are, so I will spend say period 3 on a Tuesday marking jotters.