What can I do to relieve hip pain when I sleep on my side? A pillow between my legs doesn't help.

Try a chiropractor. Try seeing a local chiropractor who is certified for pregnancy care. Many of my patients see a chiropractor to help with back and hip pain during pregnancy. Most say it helps a lot.
Different position. First, you need to be seen to determine the exact cause of the hip pain. But until then, instead of using the pillow between your legs, try a body pillow that you can put behind you and roll back on, a semi-side position. (i assume from your picture you are pregnant and can't roll forward.).