It's possible for some patients to moderate their Crohn's Disease with diet alone, but for a new sufferer with no experience with the disease, a maintenance medication of some kind is more or less mandatory.
Without insurance, the heavy hitter drugs like biologicals (Remicade, Humira) may realistically be out of your reach without some kind of assistance. Centocor (the maker of Remicade) does provide affordability plans for their meds, but I don't have the details of what the end costs look like, and that won't help with the infusion center costs. There are other drugs that are far cheaper. Some are considered less effective overall, but still work for many patients.
Do you know where your disease is in the bowel? What areas are inflamed?
I'd ask your doctor about whether 5-ASA drugs like Colazal or Lialda are appropriate for you. These meds can get expensive but in the case of Lialda at least, there is a manufacturer discount program that allows you to have your pills for as little as $10 per month (I think this figure goes up if you lack commercial insurance, to $50 per month). Lialda works very well for my CD but for others it may not help at all.
You can also ask your doctor about 6MP/Imuran, both of which are generally considered more effective than 5-ASA, and are relatively inexpensive, although I'm not sure of the exact cost for uninsured folks. I know we pay a very low copay on this one which with our insurance, generally indicates a much cheaper drug.
So, absolutely watch your diet as it will certainly keep the severity of your disease down and prevent more costly (to your budget and your health) flare ups and interventions, but it's a very good idea to take some sort of maintenance medication as well, which will keep you from some of the worst potential consequences of the disease and the subsequent hospitalizations and surgeries. It's worth looking at the diet subforum, which is here:
http://www.crohnsforum.com/forumdisplay.php?f=17
Personally, I use a low-residue (you can Google this and find lots of stuff), no-dairy diet, which works very well for me. I've been making a recent exception the no-dairy to have yogurt, which seems to help me a lot. I try to get a few different kinds of bacterial cultures at some local health/whole food stores. Seems to work for me.
Good luck to you, and keep coming back, as this forum is a fantastic source of information and advice.