Admittedly I went to an amazing piercer but mine never swelled. I'm going to have a party when she has to go to the hospital for that bullshit. Are they supposed to bleed at all?
Oral piercings can bleed, depending on the piercing location, how thick the blood is, if the blood clots easily, etc. (For example, if a person has a clotting disorder, obviously they will bleed more no matter what.)
Tongue piercings, when done properly, will bleed slightly for about a half hour, tops. Lip piercings will bleed for about a minute. Saliva has properties that makes any cuts/etc. in the mouth stop bleeding quickly, and this applies to piercings as well--this is why if you bite your lip or cheek and it bleeds, the bleeding generally stops pretty quickly. (In my experience. Caveat: I have a clotting disorder--ymmv.)
Of course, your diet can affect the body's ability to clot/bleed, as well. Alcohol, caffeine, garlic, citrus, chocolate, cinnamon and a whole lot of other foods all have blood thinning (therefore slowing the body's ability to clot blood) effects. Even medications such as ibuprofen, aspirin, and others can thin the blood. So if you've had a lot of these foods or meds in the past 24 hours, it'll affect how much you'll bleed when you're getting a piercing, no matter where it is in your body.
That said, a piercing (especially an oral piercing) should NEVER bleed THAT much. She definitely fucked something up.
tl;dr version: it's different for every person, and every body; but yes, oral piercings can bleed--but they shouldn't really bleed THAT MUCH.