Please seek the advice of a lactation consultant. The fact that the MCHN said small breasts are an indicator of low supply rings alarm bells for me - breast size has no bearing on supply so it makes me question her knowledge & opinion.
By all means pump after a feed but please don't feel dejected if you get very little out. I could never pump more than 15-20 mls ever and have exclusively breastfed two babies (and I also have small breasts).
If it was me though, I'd be ditching the pump and offering the breast after he wakes & before bed - so he is getting loads of chances to feed. Drink shiz loads of water, a full glass before a feed and a full glass after.
Hope it improves for you