okay, first: it will get easier. I am a single mom with 8-year-old twins. They were a mess and I too had dogs to walk, fish to feed and myself to care for with no help. If you are getting to stay home with him, that's the first step in the right direction.
I am assuming you live in an apartment. First thing I would do is, as long as the cat would be safe (i.e. has its claws) put it outside. It's bored. Without your undivided attention, it needs more things to do. It can still come in at night, or to eat, but put that poor thing out in the world. It will find a hobby, probably the neighbor's cat.
Depending on how big the dog is, put the baby in the stroller and strap up the dog and go for a walk. Yes, this takes more time than you will actually be out of the house, but it helps. Walk that bag of garbage out to the can. That will help. I promise.
When you are feeling overwhelmed, put the baby in the crib, close the door to the animals, don't worry if he is crying, walk outside and count to 100. Go check the mail. Go walk for 5 minutes. It doesn't hurt the baby for you to leave him for 5 minutes when he is safe in his crib. I PROMISE! THis saved my sanity and my children.
Don't worry about that load of dishes to be washed. Go outside, take a breath and count 20 things you love about life. Then go in, pick up the baby, sit him in the booster seat or bouncy seat on the floor next to you (as long as the dog can't get to him) and do those dishes. Sing the silliest song even Christmas at the top of your lungs! It will make the baby laugh and you too.
It will get better. I promise. Being single with a baby isn't easy, but if it were easy then everyone would want to do it! :) cheers, S.