No, do not write an addendum for this. You'll just be drawing way too much undue attention for a minuscule difference. It will just be another thing for an adcom to read without adding value which is something to avoid.
I'm working full time.Approximately how many months I should give for studying full time for the exam considering the fact that I want to avoid burnout?
No not at all. In fact February isn't too late for a lot of schools. That being said I would avoid sticking to arbitrary timelines if you aren't ready. Law school will always be there for you so take your time and take it only when you're ready.