Breastfeeding/leaking milk

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Breastfeeding moms:

Ellie (1month) has been leaking breast milk out of the corners of her mouth when she nurses. Is this a poor latch problem?

Today, Ellie will spit me out. And along with it, is a whole mouthful of breastmilk. Is this because of a "too fast" flow? I stopped hand expressing during nursing. And she's still having both of these issues.

Any advice?