I work full time so only get a couple of hours a day with my dd, but even then, sometimes when she's in a whiney mood, I have to look to the heavens and pray for patience, patience, patience. It doesn't come naturally to me at all.
My advice is to start leaning on your friends. Seriously. That is what (good) friends are for. When dd was born, we went through a really rocky patch - dh working all hours and I was all over the place. We have no family support, but our friends were amazing, bringing food, doing the washing, holding my hand.... I don't know how we'd have got through it without them. I would absolutely say that for about 6 months, our friendships were defined by me needing them... but then things got better, DH changed jobs, the baby got easier and I emerged from the fog of it all. The friends that helped me through it are the people I am now closest to in the whole world, and I know one day I'll be able to be there for them like they were for me.
Generally I think people like to help, but they don't know how to offer, or they don't know you need it (they're all probably saying how amazing you are for coping with everything!)
Work out what you need - a night off, some help in the evenings, whatever it is and then ask someone who you think might be able to help. Seriously, just say "i'm having a tough time, I could use a night off with a g&t, is there any chance you could have dd for a couple of hours/babysit/whatever".
Where abouts in the country are you?! If you're local, I'll help!