That sounds stressful for you

Yes, the pump can make a huge difference, but I agree with the other posters. More frequent feeds is going to help more than expressing. Many babies at 12 weeks are having 8 - 12 (and sometimes more) feeds in 24 hours, so adding an extra one or two during the day and one at night is probably all that's needed. It doesn't sound the CHN was too worried about it, so try not to be either