Hi, your mother might be having what is called subconjunctival hemorrhage or scleral bleed.
Here's a website URL that you might look up for more information about it...
MoonDragon's Health & Wellness: Eye Disorders & Problems: Bloodshot Eyes
While usually not an emergency, it is worth knowing what could be the possible cause, which might help to prevent further bleeding.
It is very important to avoid touching or rubbing the affected eye.
Hope this helps! (please
do look up the webpage mentioned)