Suffering with depression and serious anxiety Watch
Before you do this, I suggest you see your tutor and discuss your issues, they may well be able to offer you an extension without need for extenuating. If it isn't enough, you can ask them to support you in your extenuating claim. Its a good idea to try and get an extension first and to keep your tutor informed.
It might also be worth seeing the disabled students department (whatever its called at your uni) and enquire about DSA (disabled students allowance) you can claim it for mental health problems and it can help with support through uni.
I don't go to uni but i suffer from a very similar thing and it affects my work.
Yes you can, I done this with my A levels. Talk to a teacher at uni, make sure you have a doctors note and they should sort something out.
Hope you're okay x