So sorry to hear about all that you're going through. The disease is hard enough, but adding the layer of figuring out how to pay for everything makes it even worse.
It sounds like your daughter really needs to be on either EEN or prednisone (steroids) as soon as possible. My preference would be EEN, but it is very expensive if not covered by insurance. When my daughter did EEN, it was completely covered if given by NG-tube, and not covered at all if she drank it. My daughter tried drinking it first, but she just couldn't do it, so she ended up with a tube, and thus our insurance covered it. I would check to see what you would need to pay for EEN, and if it's too much, then I would ask about prednisone. The hope is that steroids would reduce your daughter's inflammation in the short term, which might allow her to start absorbing nutrition from what she eats again, without the severe nausea and diarrhea.
Another option would be to start steroids right away, but then also pursue some low-cost options for EEN. There are several foundations that facilitate donations of formula to people who need it. The one I'm familiar with is the Oley Foundation:
http://oley.org/?page=Equipment_Exchange
As has been mentioned above, you'll want to start on a maintenance medicine too, that your daughter can use for the long-term. I agree that methotrexate and imuran are both possibilities that are not very expensive.
Remicade is another commonly used medicine for kids with Crohn's, and although it's insanely expensive, there's a very good patient assistance program called Remistart:
https://www.remicade.com/rheumatoid-arthritis/remicade-support/medication-cost-support/commercial-insurance
As long as you have commercial insurance, this program pays for your co-pay for Remicade, up to $20,000 per year. The big problem, though, is that it doesn't pay for the costs of administering the medicine, and it's an infusion, so that can be quite expensive if you have to pay for it out of pocket.
There's a similar drug called Humira that also has an assistance program, but I'm not personally familiar with that program. Humira is an injection that you give at home, however, which means there wouldn't be additional administration costs.
Finally, I agree that it's definitely worth talking to the social workers at your hospital, to find out if there are any programs that can help your family with the high costs of Crohn's treatment.
I hope that you can find an effective treatment, and that your daughter starts feeling better soon.