What you mother suggests is right. You should not let the tiger balm get into your eyes. It will be harm to your eyes. If it gets into your eyes, your eyes will feel stick and feel blurry at the vision. You should wash it out as soon as possible. Just using the water, you may wash many times until it all gets out. Then you have a good rest for the eyes and waits to see the situation.
Your eyes may get hurt when your eyes get into tiger balm. If you don't take care of your eyes immediately, your eyes may get infected. First, you should flush your eyes with water until the chemical of tiger balm is flushed out. Second, soak your eyes in water and keep rinsing your eyes. Do this a few times until your eyes feel better.
Well, you should know that tiger balm is a special stuff that is used to treat some uncomfortable feelings or fly stings. Since it is a chemical product, it would not wise for you not to let it get into your eyes. Otherwise, you would be required to wash your eyes with abundant water, even go to see a doctor. So, try to use it as careful as possible ok? You gotta pay more attention to your eyes.