No, I don't think you're depressed. I think you're exhausted, and by the sounds of it your DP is exhausted also.
I was in a similar situation with my DD as DH and I have a business, but cos of horror crash section I couldn't do anything in business for about 12 months - had financial support for 6 months only (Ireland maternity benefit is crap)
Anyway, my DH got so stressed about being financially secure he worked morning till night, and even at weekends, leaving me with very hungry and badly sleeping DD, all the time - have no family nearby except elderly mum who needs me to do things for her.
I couldn't sleep as I was so exhausted and wound up!
I wish I had gone to the GP and explained how anxious and wound up I was, and asked for something, as it was, I just thought of those PND checklists and didn't feel depressed.
I now know that I had anxiety and PTSD from the birth, and there are drugs and counseling that you can do for that. I wasted a year jumping at shadows and in an exhausted fuzz.
So to answer the question are you depressed?, I think no, but you and your DP are exhausted, and you have anxiety which makes it difficult to relax and rest.
It all gets better btw when the babe starts taking solids - really things get better. It's difficult to see the woods for the trees in the early days.
Can you arrange anyone to take smallie off your hands once a week for two hours - anything? Just to take him/her out of the house so you get some time for yourself? To have a bath, a cry a scream! maybe even a lie down?
Best of luck with it. The exhaustion and anxiety is one of the major reasons why we've only had one. Our DD is 4 now and I've sort of relaxed!!!!