Oh lardy
I'm so sorry you're feeling like this. Is awful isn't it?
First of all, of course you deserve your children. You are not useless and are not a bad mum. I know that me pointing that out doesn't actually make much difference, because these irrational thoughts are driven by irrational feelings iykwim.
For me, I kind of just expected everything to be fine. I'd already had a child, I knoew what to expect, I was capable and all the rest of it, and I think I wasn't really, truely prepared for the upheval of a new baby. I too have been expecting ds1 to behave above his years, and even left playgroup because he wouldn't sit down to eat a bit of apple.
Your ds won't remember that you shouted at him, that doesn't make you a bad mum, it makes you a frustrated mum I should think, which we all are.
There is nothing wrong with you at all, and I think most families must go through this stage, maybe with varying levels, but everyone must have moments where they either raise thier voices, leave to cry for a little while, wish they could run away and so on.
It's a really crazy place to be, because I was feeling guilty about everything, and then felt silly about feeling guilty and then felt guilty about feeling guilty. Nothing was making much sense, and it was all a bit odd. I found taking all pressure of myself and ds's really helped. I set myself little tasks that I would like to be completed by the end of each day, but I no longer set time aside for them, or for ds's, I just deal with each of them as they need it. If that means that I don't read a book to ds1 everyday, it's not the end of the world, but 3 weeks ago it would have been.
I really don't know what to say to be helpful and supportive. Keep an eye on it and maybe make contact with your hv.
Hope you feel better soon.
Everyone here was so good and gave lots of really good, and supportive advice and messages, so I'm certain, they will all help you see the light at the end of the dark week tunnel. ((hugs))