So sorry to hear about the loss of your daughter.
I can't say I know what it is like but I did have a baby at 24 weeks, who luckily survived, so I do understand the turmoil of having a baby in the NICU, and how emotionally raw it all is. I can only imagine how much worse it is if your baby doesn't make it.
It must be a complete shock to find out you are pregnant.
I would suggest a few things - but please ignore me if these don't seem right.
Firstly, did A&E realise how recently you've given birth? And that your daughter was premmie? I'm not sure how quickly the pregnancy hormones clear from your bloodstream, but I think they are higher during the middle trimester than towards the end, so perhaps give it another week or two and do a home test to be sure that it wasn't a false positive from all the hormones your body is putting out. Stress can affect hormones quite dramatically so I wouldn't be suprised if things were a bit out of kilter in your system.
Secondly, you don't have to think about this pregnancy just yet. Bury your daughter, go through the formalities of the funeral and then come back to how you feel about this. There are choices you can make (about whether or not to keep the pregnancy) which I'd generally say were best made sooner rather than later, but you are in a very unusual and unique position and from the sounds of your post you have a few weeks if not a few months before you need to know for sure.
Thirdly, if you are or were in agonising pelvic pain then have the doctors looked at the possibility of an ectopic pregancy? If you're still in pain you should go back and keep going back until they take you seriously. An ectopic pregnancy can be very serious for your health.
Lastly, I'm sorry you're in this impossible situation, not only with your daughter's passing, but trying to look after your son too, going your separate ways from your daughter's father, and now the new pregnancy. Please be kind to yourself, ask for help wherever you can find it (GP, friends, family, nursery or school gate mums etc) and give yourself some time to think clearly before you act.
xxx