Weights/Exercises without using arms?

ELIZZY20

So I've just hopped back on the diet bandwagon. I'm pretty sure just that mentality of knowing I'm losing weight (I'm generally sitting around 1000-1300 calories per day, so I *have* to be losing!) is making me feel better about my body. However, I'd really like to tone up. I've only ever done cardio ... 18 years as a dancer means I've got an okay core and killer legs (and achilles tendonitis ... but that's a whole 'nuther story). But I'd still like to improve my core and get rid of my belly. (Stupid freshman 15!)

My major problem is that I am a music performance student, and I play upwards of 5 hours a day, which has resulted in my developing some sort of tendon/muscle issue. I have shooting pains down my hands/arms which turn to pins and needles if lifting anything heavier than a small book. (Wearing a heavy backpack for more than 15 minutes, for example.) To try to save my arms for what's going to make me my money for the rest of my life, I basically avoid all forms of strengthening that utilize arm muscles.

So I'm looking for exercises that can strengthen my core and back that don't use my arms. Whadda got for me?