I guess you don't have to exercise but the benefits of exercise on your heart health, weight loss, self esteem, etc, are so numerous that they outweight the reason for not getting out ther to exercise. Also if your "illness is mental not physical" all the more reason to get out there and exercise in the fresh air, the benefits have been proven on people with mental health problems.
The new recommendation guidelines are to exercise your heart (walking) 60-90 minutes/day, but you must start gradually whatever you can do. Exercise your muscles (weight training) 3-4x/week for 30 minutes. After each workout, cardio and WT, you should also stretch.
Another exercise you should take up and it can be done in the privacy of your home is to get some Yoga or Pilates tapes. I love Yoga
it really is good for you mental health, gets you in touch with yourself more than any exercise I know. Meditation is also great!
Hope this helps, keep us posted on your progress...