Sounds to me like you are feeling stranded on the island of looking after a three year old, when noone else you know is. Therefore all usual negative three year old behaviour is getting to you, and you feel like it's only you and there's noone else having to do this drudgery stuff.
Please come on here often and talk about your various problems - surf the archive board and see that every mum goes through the same trials and tribs of toddlerhood, and it is an almighty strain, even if you DO have a great support network, all the information at your fingertips, a partner and sympathetic friends. I can only imagine how crappy you must feel your life is in comparison with all those other friends who are still footloose and fancy free. You are not alone, but you need to discover that fact. There's so much kind advice and help here - it was a great place for you to start.
Please try and hang in there. You need some like-minded support, friends who have three year olds, a break by sending her to nursery. Nursery will introduce you to other mums with kids of exactly the same age, and it might be a good idea to pluck up the courage to arrange a playdate or two and get to know these other mums who might be able to offer you some encouragement. It might sound like a dreadful hurdle to breach - but I really think you would benefit.
Where are you in the country?
If you can get a handle on your feelings, and get over some of the more trying aspects of rearing small children, you will find yourself enjoying her company more. She won't be three forever.
You could try the "Little Angels" approach of "Fake it to make it" - over the top smiling and positive praise (even when you don't feel like it) but see the impact it has...