Congratulations!
I think you're doing the best thing by being there for her, letting her know that she's not alone with this new situation, and that the three of you are together in this as a family. Three weeks is still very early days, and lack of sleep makes people react in weird ways (especially with a PFB, when you're suddenly responsible for this little precious being for the first time).
I couldn't have got through our first-born, who was a right old screamer, without the help of my husband, both practical and emotional (I did the night feeds, he did the nappy changes when he was there, we alternated the walking round/singing(sh-sh-ing, but more importantly, he was knackered as well, so understood how hard it was for me).
So you're back at work now - what can you do:
Organize a cleaner, if finances allow (and DW agrees).
Take DS as soon as you get back in the evening (DW will have been with him all day). Give DW a small glass of wine (or a big one, whatever), stick on some good music, and tell her to relax, you'll walk round with DS for a while (or watch out for him if he's sleeping).
While he's this young the two of you can still go out in the evening, and take him with you - Make the most of it. We took DD1 to some strange stuff before she was 6 months old and started needing a regular bedtime - parties, concerts, restaurants etc. Make sure you bond as a family (which you're clearly eager to do).
I remember reacting really badly when DD1 was 4 weeks old, went out in a huff for a few hours (leaving her with DH and friends), came back and DD1 was screaming (again). It looked really bad from the outside, but it was a natural reaction to the extreme circumstances that got better soon afterwards. It was very different when a friend of mine got PND years later; her reaction was much more subtle and difficult to spot, yet it resulted from loneliness in a difficult situation.
Best of luck with it all.