Oh Shish, please don't be so hard on yourself. I had a really helpful Mum and lovely DH who was working from home when I had DS2 and I still got PND. Its nothing you've done or haven't done its an illness and it just needs treating that's all.
I really think you should go and see your GP asap, or if you aren't happy to do that, call your Health Visitor for a chat or to arrange a home visit, as they are also trained to help with this sort of thing and will be able to advise you.
Do you ever get to take a break from being Mum? I know your baby is only 13 weeks but think of that in terms of months and you are overdue for a break, even if its just an hour or so to either go for a walk in the sunshine, go shopping or even have a bubble bath and an early night. You might be a mum to two little ones, but you are still you and you need and deserve time to yourself every now and again. Honestly, it will help you to be a better mum.
It will get better, I promise, but you need to get some help from your GP or Health Visitor and take some time for yourself.
I know and understand exactly where you are coming from with the wishing you had stuck with one child, I've been there myself but your DSs are going to be great friends - a real little team and one day you will be watching them play and realise you can't imagine ds2 not being there. My two boys have a slightly smaller age gap, they fight like cat and dog sometimes, but they adore each other as well and are practically joined at the hip. Having a brother will be such a precious thing to your ds1, someone to share holidays and playtimes with, whisper to after lights out, someone to play board games and football with, a best friend who is always there. Try to keep this in your head and look to a happier future. It will get better, just look at me, 5 years ago I was where you are, now I have 2 gorgeous boys and a beautiful dd.
Please book that appointment or make that call.
Wishing you all the best.