Insatiable baby = supply issue?

Shema N

My 1 week old LO has been nursing practically nonstop since last night and this morning he's going a half hour between feedings.

Could this indicate a supply issue?

I'm also really worried that he's leaving such little time between feedings that my breasts don't even have enough of a chance to fill up befre a feeding. Is this something I ought to worry about? I tried pumping after a feeding today for 10 minutes and couldn't even get an ounce out.

Help! I'm freaking out!