Is using an answer I posted online on Math.SE considered plagiarism?
I'd like to know if using my current answer would be an academic offense.


It's impossible to determine this without more information about your university and course policies.  If you're honest about what happened, then I doubt you could get in a lot of trouble for this, but of course I don't know the policies and potential consequences in your case.  At my university different courses can have different policies on collaboration (regarding what's allowed and what sort of acknowledgment must be given), but they should be explained at the beginning of the semester.

If I were teaching the course, it wouldn't bother me that you got advice on this problem, since it looks like you did most of the work yourself and learned something from the feedback you received.  However, I would be unhappy that you posted the homework problem and a complete solution online, thereby making it easy for other students in the class to copy your solution if they know about math.SE.  If the grader detects several solutions with nearly the same wording as the one you submit, then you may all be accused of cheating.

If you can't find a clear statement of the relevant policies on your course or department website, then I strongly recommend asking your instructor how to handle this.  In theory that could end badly, but I don't expect it to.  Bringing it up yourself is almost certainly better than letting the instructor discover it, and it would mean you could stop worrying.