relax.
Feed a baby on-demand. Yes, and before sleep and after waking.
Do not feed according to a 'schedule' because scheduling feedings do NOT take into consideration that a baby's appetite varies and does not take into consideration their growth-spurts and that each baby even 'cluster feeds' which means they even feed every single hour.... and this is all normal.
Feed on-demand.
I breastfed both my kids, they would need feedings every 3 hour so less. This was for the 1st year. It was feedings on-demand 24/7, day and night.
NOT all babies, display 'hunger' cues.... blatantly. So you need to know your baby.
And MANY babies do fall asleep after feedings... normal.
A baby does get tired after about 2 hours after waking. Then they feed. Personally, a more sane guideline is:
baby wakes
feed/nurse
baby is awake
2 hours later or so, baby gets tired.
Feed before nap or sleep
baby sleeps
baby wakes after nap/sleep
feed baby
baby is awake
2 hours or so later, baby gets tired
Feed before nap or sleep
baby sleeps/naps
baby wakes after nap/sleep
feed baby
etc.
"Playing" before sleep... in an infant... or child, typically gets them more stimulated... OR "over-tired, and thus, they cannot sleep/nap well.
A more sane thing is:
after baby wakes, feed/nurse him.
then baby is awake
then baby gets tired... then nurse/feed him again.
"Playing" does not mean he has to do all sorts of 'activities." At this age, even a bath is a major activity for a baby and they get tired. Even just hanging out, is busy for an infant.
Babies this age, get easily over-stimulated as well. Being over-stimulated then causes over-tiredness. Over-tiredness actually makes a baby/child unable to sleep well and to fall asleep well and to stay asleep well.
next, when your baby 'wakes' from a nap after 45 minutes... is it really him 'waking' or you going in and waking him just because he makes noises or stirs while sleeping? There is a difference. For example: if he is just stirring/making noises (but is not crying), then try and let him be.... he may go back to sleep. But if you interrupt this process... then he WILL wake wake up. That is how my son was. He'd stir/make noises while napping... but if I let him be and let his rhythms of sleep just be... he would on his own fall back asleep. So I didn't "wake" him just because I heard him stir. BUT, If I WOKE him up just because he stirred or made noises... then he did NOT get a full nap.... and he was actually still tired.
So know... your baby's rhythms... and cues....
Of course if your baby is waking up crying.. then go get him, comfort him etc., but, he may go back to sleep. Unless you then interact with him immediately and get all active with him.
I always nursed my kids as babies when they woke up, on demand throughout the day and night and before any nap/sleep.
My kids as babies, often got tired before 2 hours. So... the bottom line is... that is how it is sometimes. Everyday is different.
As a baby/infant... the whole day is spent on feedings and their naps.
all the best,
Susan