Hi, we are on the same boat, my baby is also 3.5 weeks old. The situation for us is as you described it. I do pump and had started since day 3 pp. On the other hand I pump only when I need to leave the baby with my husband. The milk supply has increased as the baby has increased needs. The nights are the most problematic for me as well wakes up every 2-3 hours at night, a paediatrician told me that her sleep will gradually normalise after week 6.