I am 309 Ibs 6 foot 2 inch and I have been doing BJJ for about 1 1/2 months now. I started at 330 pounds and have lost a ton of fat and gotten stronger. My stomach has come down a couple of inches and my chest and arms have gotten a lot stronger. My cardio compared to my first day is immensely improved and my reflex's and agility off my back has vastly improved. My advice is because of the condition you are being in I would clean up your diet which will make you feel cleaner and healthier and also incorporate yoga into your daily routine to stretch b/c Im sure your not very flexible etc due to your weight.
I also suffer from severe depression, bi-polor, anxiety with paranoia have ADHD. I take daily medication for anger due to my severe bi polor dis order, depression medication and anxiety medication along with medication for low testosterone and hypothyroidism so I know what its like to have severe mental issues.
Having said all that in the last month I have felt amazing, better than I ever have. I have grown calmer and more restrained, stopped angry outbursts and have not been depressed. Because of this I have embraced BJJ in the short time I have been practicing and the cleaner lifestyle it seems to incorporate. I understand I have only been doing this for 1 1/2 but I have not felt this good since I was in the Corp running around young and dumb lol.
I can GUARANTEE you can do BJJ, 99% of the effort is just showing up to class. You've taken the step to look to a forum and post a question so your interest is there. Now you just need to go a gym and take that first step to improving your lifestyle as a whole.