She is very very little still, it's not unusual for babies this age to need help to sleep and only take longer naps with baby wearing. Around 3wks the newborn sleepiness wears off too which might be why you can't just lay her down for a long nap anymore. There's also a big growth spurt and developmental leap around this time which disrupts sleep too.
I would suggest just trying to get a small gap between feeding and sleeping for now, even if it's just a nappy change so try to keep her awake on feed if possible ...then a short awake time (just burping and a nappy change probably) then for a nap in the sling just to get into a routine. It will be easier to sleep train for cot naps when she's a little older.
A times are really short at this age - no more than an hour usually, including time to fall asleep so I'd try to get her asleep around that time after waking.