Can I shave down there if I have a yeast infection? What are good body washes to use on your body and private area?

No. Shaving the private part is not a good idea. If will not help the yeast infection and may predispose you to getting infection in the hair follicles. Visit this site for suggestions about treating the yeast infection.
Wish you good health! - Have a diet rich in fresh vegetables, fruits, whole grains, milk and milk products, nuts, beans, legumes, lentils and small amounts of lean meats. Avoid saturated fats. Drink enough water daily, so that your urine is mostly colorless. Exercise at least 150 minutes/week and increase the intensity of exercise gradually. Do not use tobacco, alcohol, weed or street drugs in any form.
Practice safe sex, if you have sex.
Shaving OK, any soap. Shaving should be OK during a vaginal yeast infection. Any soap is just fine in the genital area. Just don't douche (with any kind of product), which is bad for vaginal health.