I think the other answer is a bit more scolding than is necessary.
Your professor has your email to your mom, didn't comment on it, and forwarded it to the person responsible for recording grades. It sounds like what you are worried about is not a worry to the professor, and it sounds like your professor is quite a reasonable person where technical issues are concerned (i.e., by accepting your evidence that the work was done).
If I were in your position I'd concern myself more with making sure your submissions are fully accepted in whatever software you are doing the submission with in the future - hopefully the software provides some sort of feedback or way to check.
You can also consult the course syllabus to see if there are any specific policies on what is allowed and not allowed for exams. I don't think you are crossing any lines by asking for proofreading help (presuming you are not taking a course where proofreading is a major skill that is being taught). I also don't think it is necessary to explain yourself to your professor unless you find a written policy that makes what you did clearly against the rules: by sending the email, you haven't made any attempt to hide what you did so there isn't really anything to come clean on.
Besides that, I would stop worrying about this and focus on any other studies and responsibilities you have. You're doing fine.
I'm taking a class this semester through an online program. We have an essay exam due on Thursday every week that is open-book, open-notes, etc., we're even asked to cite the textbook and other course materials. The professor emails us the question or questions two weeks in advance.
I've been preparing my essay responses ahead of time, then submitting them after I open the exam, I work 2 jobs and so I rarely have the time alotted to sit and write the essay, I figured this was ok since it's open-notes. Last week I was slammed with work and didn't have as much time to proofread my own essay for grammatical errors so, not really thinking of it as a test so much as a regular essay, I asked my mother to look it over and sent the rough version to her in an email, she found one sentence fragment and on run-on sentence which I only changed when I put the exam into the online submission portal.
Jump forward to today, I was trying to look up my grade and there was a note saying there was no submission for my essay exam. I knew I had submitted it but freaked out and in a rush, emailed my professor offering to send him the email sent to my mother (early in the day on Thursday) as proof that I had basically finished the essay Thursday morning so there was no reason not to have submitted before it was due that night. (We get no confirmations on submitted work and there are no timestamps on past work submitted online) I also sent him the word document on my computer with the basic essay, pre-changes. He responded basically just saying he would forward it to his grading assistant, and that's it.
My question is, could I get in trouble for cheating since I had my mother proofread the essay ahead of time? I have the emails from her proving she only looked at grammatical stuff but it didn't occur to me until after I sent the email this morning that this could be considered academic dishonesty since it's called an "exam" and technically I received outside help. Thoughts?