Less than an oz *UPDATE*

My first two pregnancies I didn't get any milk in at all. This time, I actually got milk in and I'm trying SO HARD to breastfeed! I'm pumping all.the.time. but I get less than an ounce. Before he drinks his bottle I let him latch for a while. A couple times he came up with a burp and milky face. Sometimes when I squeeze I get a squirt, other times not even a single drop surfaces. The lactation consultant said keep pumping it's "supply in demand" but I'm afraid my one breast has dried up completely despite my efforts.

When should I throw in the towel? Should I just keep pumping? Is there a chance my supply could come in? He's 10 days old now. Is it too late?

*UPDATE*

Girls, thank you so much for your advice! I have a slight stream going now!!

But now...baby is frustrated and won't latch. It's hit or miss.

Yesterday he nursed at both breasts for one feeding which was the most success we've had.

How do I get him to latch more frequently?