BigGiantCow you are feeling really negative, but I think with good reason! Staying in with a three year old in this terrible weather does test your patience, I don't love getting down on the floor and playing with my children either, but I don't thknk that makes me a bad parent.
I would say a couple of things: aim for being 'good enough' mum, not perfect mum, you can't be perfect and won't always want to do what a three year old is doing all the time, so if your dd goes to bed having had nice food, kept safe, some cuddles and nothing terrible has happened, then that's a 'good enough' day. You can be Supermum on another day.
Also you probably look together to your friends, so your friend may be experiencing all kinds of things that you dont know about. In my experience, many people feel they are putting on a front, especially mums at home, because very few people are saintly earth mothers which is what people think you have to be.
I think working out of the home may help a lot, I know it's more to juggle, but interacting with other grown-ups and doing purposive tasks other than repetitive cleaning and playing dolls with a three year old can be good for your mental health, or it was for mine anyway.
Cleaning- I am crap at this, but have got some good tips from the FlyLady site, it's full of her ridiculous homilies but it is good for breaking down housework into small manageable chunks so it all seems less overwhelming.
Finally, I would get your PMT sorted, what's your eating like? I found my moods were terrible until I stabilised eating, so eating little healthy and often rather than going ages and eating a choccy bar. Hope the doctor can help on this one.