My first thought was, "Get to Zappos.com immediately and get a pair of closed-toe low-heeled pumps."
I found this definition of business dress/casual:
Business dress for women means a suit or tailored dress in conservative colors (black, gray, beige) with low-heeled, closed toe pumps and conservative jewelry. For men, business dress means a conservative suit, not a sports coat, plus a long-sleeved shirt, tie and leather oxfords or loafers.
Business casual means a tie isn't necessary. Khakis with a long-sleeved shirt are popular. For women, it's a dress, skirt and blouse, or slacks and blouse with flat heels allowed.
I'm sure you're required to dress nicely for school, so that should handle your daytime wardrobe. I would definitely wear a suit or dark color dress for dinner.
On the needles: Tempting for Kate, cabled jacket for Emma