Hi Eliza, first of all congratulations on your DD 
Sorry if this is long, I just want to share with you how I felt, and let you know you will be fine 
A lot of what you're saying sounds like how I was a few years ago.
My DD is 4 now, but from around 3 months after her birth, to 12 months, I was absolutely full of anxiety. I convinced myself I had cancer and that I was dying very soon.
I told nobody how I was feeling, in my head I didn't need to talk to anyone, I was dying and nobody could stop it happening.
It got worse and worse until one day I couldn't keep it in any more and broke down, my family were shocked when they realised how bad I was feeling.
They persuaded me to see the GP, I was hysterical telling her I had bad pains in my legs and that I was dying from cancer, she gently told me "No lovely, you're not, you are suffering from anxiety and depression"
I know you are in the midst of it right now but honestly we all believe you and your children will be absolutely fine, I completely understand how you feel, and you won't believe what anyone says because what's in your mind feels so real. It isn't.
Please please talk to someone, your husband, family, friends, someone in RL and get help sweetheart. I suffered (and still am these years later) and I cannot bear for someone else to suffer so long the way I did.
Please, you will be ok honestly, just try to get some help for all your sakes 