Is homeopathy effective for styes?

Yes, can be. Classical homeopathy can indeed help with stys. There are over 100 remedies that might be the one you need. A well-trained professional homeopath can select the most effective one for your case. In the meantime, you can apply warm compresses to your closed eye for few minutes 3-4x/day. See eye doctor if it's not resolved within a week, or you also have fever or vision problems.