oh dear, how horrible for you all.
You are certainly not alone in this. It is so, so hard. The memories are fading now, but I remember how the year after DS arrived everything seemed to go wrong, I shouted at DD, lost my temper all the time, fell apart generally. But things did get back on track, and it did get easier.
First off, please ask your HV for some help.
You say the house is a mess, don't have energy to play with DD, act roughly with DS. The last of these really has to stop, doesn't it. You can't be rough with a baby.
Do you have a sling, or even a back carrier? It might made DS feel better and leaves your hands free.
Does DD go to nursery? she should get funded sessions, and it will take some pressure off you.
About the house - in what way does it upset you that it is a mess? Is it because you are houseproud normally, or because you think it ought to look tidy and is a sign of failure? Either way, this is not normal times. This is a difficult period when your efforts need to go into looking after you, DS and DD.
How much does your DH help? Does he know how you feel? If you can, please confide in him - you need support and help from all sides, not the extra effort of concealing how you feel.