As BB's said, it's not fair if you're in thrall to the delectable tiny tyrant 24/7 while he gets to carry on as if he's a single man with no responsibilities.
If housework builds up - turn a blind eye and leave it. Do you what you need to do to have clean clothes for yourself & pfb, clear a path in the kitchen (sod what's in the sink - wash up only those items you need) so that you can make a snack/drink for yourself, and let him sort himself out.
Allow the hoover/brooms/mops etc to grow cobwebs until he uses them.
No-one ever died of taking a shower/bath in a dirty tub and cleaning the bathroom and the loo is a job for him. Get him a pair of Marigolds, bathroom cleaner, and a bottle of bleach, and set him to it.
Either send him out with a detailed list and map of what shops to go to, or shop for groceries/veg/loo rolls/household bits and bobs online.
If you're b/feeding, lie down on a bed with pfb between you and the wall (or their cot) and let them graze while you doze - a 5 minute nap can make a lot of difference when you're brain-addled through lack of sleep.
If you feel up to it, try to get out in the fresh air as often as weather permits - not in the car but just taking pfb in their buggy/sling to the park or local shops for half an hour a day as it's easy to feel isolated when you're indoors 27/7.
Make the most of whatever time you can grab for yourself either chilling on the sofa, mumsnetting (combine with b/feeding in the early hours), or just catching up with much-needed restorative sleep.
By the time pfb is 3 months you'll have it all down to a fine art - and will have hopefully kicked dh's arse into touch too.
Tip: don't expect him to clean to your standards immediately as what you can do one-handed may take him years of practising with both hands. 