The practicalities of taking your children out will get easier with practice and as time passes. At the moment, I imagine that being depressed makes every obstacle or difficulty seem insurmountable, but maybe knowing that the obstacles and difficulties will get better might help you a bit now - I hope so.
I had PND after each of my three ds's were born, and looking back with the help of a psychotherapist, I now realise that I have been depressed since I was a teenager. Apparently it's not normal or ok to think about commiting suicide when you are only 14.
I'm on antidepressants, which do help a bit, but I have been aware for some time that I can get housebound very easily. We moved to scotland in the spring of this year, and before we moved, I had a group of friends who used to come and see me regularly - barely a day went by without at least one of them rocking up to drink coffee with me - which was great in one way, because I had company and support, but not so good in another, because I had little reason to leave the house.
I remember feeling the way that you do - I was in a flat with ds1 who was only 1, in a new town, knowing no-one, shy, and finding it a struggle to get us and the buggy in and out of a first floor flat. We had lovely neighbours who invited me to drop in any time with the baby, and offered me the use of their garden for a paddling pool, but I couldn't summon up the nerve/energy/resolve even to walk across the road to them - and I know I'd have been welcomed and would have had a good time if I had.
Since our most recent move, I have become somewhat reclusive. As my children are older - too old to need me at the school gates - I don't have that way of meeting people (the school gate is a great place to make friends, I promise you), so I have to find my own ways to meet people - and it has been a real struggle. I have joined an art class, and just before christmas, I met up with 2 other Glasgow mumsnetters and went across to the Edinburgh christmas night out - which was great. It is going to take time, though, and I can empathise so much with how you are feeling.
I would second the advice to consult your gp. There may be counselling available to you, or you may find that antidepressants help you get through the next few weeks and months until things feel a bit better.
I will keep an eye on this thread, and am more than willing to offer whatever support and advice I can.
Hugs.