When does your games design work need to be in?
Speak to your personal tutor (if you have one... at my university everyone is assigned a personal tutor who is the first point of contact for academic and welfare issues) who should be understanding and nice (I've had mental health issues and I'm about to repeat my second year, but my tutor has been brilliant, calling doctors to make appointments for me so I could get a doctors note, and even being behind me when I wanted to transfer to a new university) especially if you tell them the issues you've had. They'll be there to discuss all your options and set your mind at ease and to help you get in touch with the right people to sort it out, including if you feel you need a gap year (it's normal when there are health issues involved and several people take them).
Good luck with switching to illustration!