This phase I/II trial studies the side effects of enzalutamide and indomethacin and to see how well they work in treating patients with prostate cancer that does not respond to treatment with hormones, has come back, or has spread from where it started to other places in the body. Androgens can cause the growth of prostate cancer cells. Hormone therapy using enzalutamide and indomethacin may fight prostate cancer by lowering the amount of androgen the body makes and/or blocking the use of androgen by the tumor cells.