I understand this feeling entirely. I also made use of extenuating circumstances when I was at uni, and felt a little guilty about it for years. Eventually, as I learned more about my own mental health, I came to see that it was completely valid - and frankly, I was surprised I didn't use it more!
Your professors will understand this, and they'll have seen it all before. Extenuating circumstances are there to be used, and your lecturers and tutor would rather you get a fair whack at the grade you deserve than see you pass up on EC because it feels like "cheating". Honestly!
If you're worried about them getting the wrong impression, though, talk to your lecturers and your personal tutor. Send an email or grab them after a lecture/seminar and thank them for their flexibility. People respond much better to humans than they do to impersonal form submissions.
They'll respect you for taking the time to talk to them properly - and they'll be able to reassure you that it's okay, as well.
Best wishes,
Matthew (Yipiyap gap year rep)