No, it is not. Subconjunctival hemorrhage is a common cause of painless bloody eye, which is usually noticed by someone else or when you look in the mirror. The bleeding results from a break in a small blood vessel in the sclera, the white of the eye. It would occur with heavy lifting, coughing, sneezing, and vomiting or for no reason. On the other side, medical conditions that can occasion cause it. Yes, it looks bad but not dangerous, which would leave no residual change in vision. It would return to normal within three weeks as the blood is absorbed. Hence, it does not require any treatment. During this healing period, your sister had better avoid any causes as said above.