It may be a case of colic, but that doesn't usually start this early. It could be because you aren't using the right formula. Some babies just have an intolerance to the milk based formulas and need something that is either lactose free or for sensitive tummies. It would seem that this is the case because of the vomiting and the incessant crying.
Your baby should not need to eat more than a couple ounces every 2-3 hours, or 50ml every 2-3 hours. 100 ml (4 ounces) or more is way too much for a little baby, so no wonder it's all coming back up. Babies who are twice your baby's size or over eat about that much. 50 ml every 2-3 hours is merely a guideline however so it is possible that she might be hungry, but first do this:
Babies will cry and suck at their fingers not just because they are hungry but because this is how they console themselves. With that in mind and before you run for another helping of formula:
Check her diaper and change it if it needs it. Some babies are more fussy than others when it comes to a wet nappie.
Check her clothing and make sure there are no places that could be causing discomfort, such as something that is too tight fitting.
Too many or few layers of clothing: she might be too warm or too cold.
Check her toes: many babies get pieces of thread or hair wrapped around their toes or fingers and it becomes very painful and dangerous.
She might just want to be cuddled. Try swaddling and or rocking or walking around with her. Taking her outside for fresh air helps too.
Of course you already covered the burping part, but the change in formula will help with the gas: you can also get baby gas drops or gripe water which sometimes helps with that.
Finally she might also be just over-stimulated and need some alone time. For myself I never understood this until my most recent baby (number 6) would decide she'd had enough of me and wanted to be put down in her carrier to rest on her own.
I hope these tips help....I'm doing it from experience and memory of what I've read, so I hope I didn't miss anything.