CarrotCakeCrumbs, great name. You are absolutely not selfish to feel like this. We are allowed to feel what we feel, that doesn't make you selfish. Don't feel guilty either, kids are bored, they are always, its a natural part of childhood, it doesn't harm them. Being a bit bored is actually very good for them, they learn to self occupy because of boredom.
It sounds like you feel you are failing, and that you should do more for your family. Can I ask what your DH does to support you? Does he fully understand how you feel? IME men sometimes need us to tell them what we need them to do, be it help with the kids or house or even just a hug. What happens if you ask for help?
But, it will get better. Getting outside is a huge boost to my spirits, can you wrap up warm and get out even if its for a walk? Do you have anyone in RL you can talk to?
The other thing that helps me is to escape in a book or a film. Even when DC were same ages as yours I would let them snuggle up on the sofa with me, them watching rubbish, me reading a book. Self care helps too, set aside some time to do one self care thing a day such as a long bath, hair, nails, yoga or some other activity that benefits you, and just you, and don't feel selfish or guilty. You need to look after yourself, because you are looking after everyone else.
(((hugs))) I'm depressed too at the minute, its crap, but I will get through it, you will too, just little steps each day.