I take coumadin and it has caused my hair to start to fall out also. I decided to become a "hat" person. I went to TLC.com, a website that serves women undergoing hair loss due to chemotherapy. They have a wonderful, inexpensive array of hats. I bought about 8 and now I wear one every day. I also changed the style of my hair, which helped a little.
Like someone said before me, "it's only hair!"