3 months = growth spurt = increased hunger/feeding frequency/intake amounts= 24/7 = day and night.
Also may include: Cluster-Feeding, which is when a baby needs to feed even every single hour. NORMAL and both my kids did that too.
Her only getting 2 oz. per a bottle. Well, maybe switch to a faster flowing nipple. She is now 3 months old, and a newborn nipple/slow nipple is something she probably may have outgrown.
Feeding... in a baby by this age, they are more 'efficient' feeders and suck more efficiently and thereby, feedings may get shorter per session. Commonly at this age/stage, the breasts do NOT feel 'full' nor get engorged because they have been adjusted to your baby's feedings and amounts. Normal.
Feed with BOTH breasts per session. That is what our Pediatrician and even my OB/GYN said. My kids drank me dry, from both breasts, per session.
My kids ALSO nursed, every 2 hours or LESS.... per growth-spurts. NORMAL.
Always feed on-demand.... when at home and with her.... or yes, your milk may begin to lessen/dry up.
Your milk production, SHOULD produce according to your baby's feedings and frequency and amounts.
Does she have enough wet diapers? if so then she is probably getting enough intake.
Just because she is falling asleep at the breast, does not mean she is a
lazy eater... it may just be, that she is full. Full babies.... often fall asleep at the breast, after nursing.
DO you actually hear her swallowing or see it???? If so, then she IS sucking/latching on properly. If not, maybe her latch, is not good.
If anything, ask a Lactation Specialist....
all the best,
Susan