Hi Katrina,
I am new too, with a 15 week old girl, it's a baptism of fire isn't it
. I hear you 100%!
Puppy may be overtired from not being rested consistently enough during the day, thus driving you all a bit batty for attention. If you google it there are tables online showing how much sleep they need and t's a lot at this age, I can't remember but up there in the high teens (number of sleep hours advised), even though they are all fired up.
From reading your post, the real concern is giving you all a bit of a break and establishing a more balanced routine. If you can try to keep to a rough schedule of crating it may help a bit e.g. have really set times during the day when you crate, come hell or high water, perhaps cooking/mealtime, school home-time, i.e. when it's busier. An hour here or there are what works for your schedule and busy household. Getting puppy used to calming time on own in a quiet spot is a good thing, a definite skill for them to learn. Ours grumbles for the olympics at first, lol, but now settles after a minute and takes a nap. She has learned that I will return and is becoming used to it.
You could try a beef trachea as a crating aid (sounds grim but is essentially a dried hollowed out chew-stick type treat which has health and dental benefits) is something we introduced at 14 weeks - puppies from 12 weeks can chew on them without issue - you will find them online. It looks like a battered old opaque rubber windpipe. Ours will happily spend 20 mins chowing down on that in her crate, and now actually prefers a quiet spot to get stuck in and indulge. We reserve it for crating time so that she associates it with time to chill. You could try one, you never know, your puppy might also find them as irresistible as ours? When crating during the day, I also close curtains and put on radio 4 down low, lol - sounds bonkers but it creates a relaxing atmosphere away from the human motorway
that is our kitchen area.
Only very recently we have noticed a big change in behaviour, really quite startling - puppy has gone from bonkers cockerdile needy mode to much calmer, dare I say it, more mature mode. I am so grateful that the posters on here were right - puppy will start to calm. I now believe it, so keep the faith.
It sounds like you are doing so many great things with your puppy, I empathise with the sheer constantness of it all and exhaustion of early days, but I'm sure you will start to turn a corner soon. Best of Luck