Is my circumambulation and Hajj valid, given my doubt about the discharge of something—I don't know if it's urine, moisture, or sweat—upon leaving Arafat, and my uncertainty about its impurity when I went to the restroom due to the intense crowding?

You are not required to purify your garment as long as you are not certain about the impurity of the discharge mentioned, because the default state is purity. Since you performed ablution before the circumambulation, your circumambulation (tawaf) and Hajj are valid, and there is no need to doubt that.