I can relate. I have been depressed for a year now, plus was out of work for months and I know I'm doing little around the house.

When I was home I wasn't even feeding the cat (don't worry, my son and wife did it). Also not taking a shower or changing my clothes.

My family was frustrated with me but I just had to repeat myself and explain that I was under a lot of stress being out of work and the depression was doing it's thing.

I did however find that I could lower their frustration with me if I did certain things around the house. Call those things "low hanging fruit" - things that are easy to do but are very visible and show that I'm doing stuff around the house.

I made a schedule and stuck with it. It was all simple stuff and I often did it all together so the rest of my day was free. The schedule allowed me to see what was coming so I could work myself up for it. And when I was done I had a sense of accomplishment. Plus the family was happy things were getting done so everyone won.

You have to cook and clean and do a lot more, but maybe a schedule will help. That way you can hit the high visibility stuff and still have time for yourself.