I'm sorry you're having a tough time, and are so anxious about how you will cope. If you are concerned about AND, you are doing the right thing to talk to your GP.
I've just had DD3 (5 weeks). DD1 is 4 (starts school in september), DD2 is 2. I also worried a bit when pg about how I would manage. DH works away part of the week, so I was really worried about how to get them all ready in the morning / at bedtime / cook meals with the baby around.
Guess what? I'm doing it. It's not perfect, sometimes I have to accept that someone will not be happy (whether the baby is crying for a few minutes, or one of the older ones is feeling a bit fed up because their tea is half an hour late, or I can't play with them immediately, etc), but I'm doing the best I can, and everyone is getting along together and is happy most of the time.
I am running around all day, yes, but it won't be forever.
Going out is a bit of a mission, so I tend to keep shopping trips to when I have less DC (e.g. when DD1 is in preschool / DD2 in nursery), or when DH is around. I also tend to feel stressed about BF in public, and if DD3 cries. However, for my own sanity, I keep telling myself that I have the right to go out in public with my baby, babies cry and need feeding, and everyone else will have to live with that - after all they were all babies themselves once! I tend to talk in a calming way to the baby, which also calms me down, and shows anyone listening that you are doing your best! Just stuff like "oh dear, you're hungry / tired. We'll just finish in this shop, then mummy will feed you / take you home." etc... I also try to breathe in and out in a calming way if I'm getting really stressed. I've had lots of sympathetic looks and kind comments when DD3 has been crying and we've been out - I think people are more tolerant than I expected!!! :) When I need to, I BF when we're out, and no-one is really looking TBH. I think once people realise you are feeding the baby, they tend to keep their eyes to themselves - if they don't, well, that is their problem not yours. It is also possible to time short trips out so that I feed DD3 before we go, so I don't have to stop and BF during the trip (stopping to BF really stretches the trip out, as DD3 can be a bit slow feeding...).
My HV has said she would refer me to Home Start if I need an extra pair of hands every so often - maybe this would help you too?
Hope the GP is helpful.