It sounds like your Jack is what they call a "catnapper". It is SUCH hard work, you never get a break - even to do the basics like eating.
My daughter did the same - she is now 4 and a half months old and she has gradually increased those 20 minute sleeps to about 3x 40 minute ones(thankfully!!!!).
My advise would be to not fight it and try to 'make' him sleep. Wearing him in a sling is a good idea. You might have to hold him while he sleeps for a while. Alternatively if you are into co-sleeping lie down with him in your bed and see if he'll have a longer nap with you.
I also found getting out of the house to be important - it's impossible to entertain a baby at home all day when they are awake for nearly all of it. Put him in the pram and get out of that house!
I got a lot out of reading Pinky McKays book Sleeping like a baby.
Bookmarks