Nosebleeds can happen due to many reasons -- it could be due to overly sensitive blood vessels that burst and bleed (such as in warm, dry weather), infections of the nose, throat and sinuse, common colds and flu or allergies. It's quite common in young children and most of the time it's nothing to be worried about. Since it has happened twice since his birth, that's quite a huge gap so i reckon it's nothing to worry about too much for now. Just monitor baby and see if it starts becoming a regular occurence. If so, seek medical help.
Your child can't help but swallow some blood due to the nose bleed but a little is not dangerous. He might get nauseous and vomit the blood out.
Bliss Ang