I don't know if you have PND but if you aren't getting any help with the Dr. do you have any other support? Any mum-baby groups? If you manage to get out to these groups, often they can make you feel "normal". Lots of people (almost everyone) feels the first few months (and beyond) hard. It does get easier, but if it doesn't for you, hopefully you won't feel afraid to ask for help again.
Everything you've described sounds normal to me. Shouting at your baby when you are utterly exhausted is a normal human response. Having anxiety is quite common too. Do you feel an overwhelming protection for dc? As if something might happen to her? Or is it a feeling of dread and "I can't do this"?
I know it must feel hard sometimes if baby isn't settling and you are getting more and more tired, especially if DP is working late too, but those symptoms you describe can be just normal things that happen when you become a mum.
I would keep an eye on yourself (which is what you're already doing), get some RL practical help - someone to have baby whilst you catch up on sleep. And stop being hard on yourself when you have a shit day! Some days will be great others not so, you go to bed and hope tomorrow will be a good one!
I've had friends with pnd and the symptoms they had differ to yourself. There was also a general depressive feel to their illness, which they couldn't "shake".
If you are silk worried, seek a 2nd opinion or talk to your HV that's what they're there for.
DD is 10 weeks. I love her to bits but I am anxious quite a lot of the time. She is difficult to settle in the daytime and so I get no time to myself. If she does sleep, it's on me so I can't do anything. She also has reflux, so there can be a fair bit of crying due to that as well. The last couple of days have been really bad, on Wed she was awake from 1 in the afternoon until gone 8 at night, and I just couldn't settle her. She got very overtired and I'm ashamed to say I shouted at her, DH was working late and I was just exhausted. So I bit the bullet and went to see GP today, he said he didn't think I was clinically depressed, made me do the depression score thing which "showed something" then said that if I felt really out of control or suicidal, to let them know and then there were "lots of things we can do".
I'm just concerned that maybe he didn't ask the right questions and doesn't realise how hard it is. . I don't want to be suicidal before I get help!