It is possible. It is universally known making-ups may do harm to skin. Thus, eyeliner is also possibly harmful to eyes and makes them uncomfortable. Twitching is one of those discomforts. In specific, there are two reasons that eyeliner may cause discomforts. First one is the friction between eyeliner and skin. Skin of eyes is the weakest among the skin of entire body. Thus it is also the most fragile parts. Using eyeliner too often may bring bruises on skin of eyes, especially eyeliner pencil as it is hard and sharp. Eyeliner liquid is better. Second one is the chemical substance in eyeliner. In order to achieve the desired color and lasting time of eyeliner, manufacturer put some additive in eyeliner. Generally, the additive is Ok. However, eyeliners of low quality may contain heavy metals such as lead or mercury. These metals are harmful and poison. All in all, your mother may be right. Do not use eyeliner too often and use good ones when necessary.
Till now, i didn't heard that eyeliner can cause eye twitching. Eye twitches can be result in many reasons such as stress, tired eyes, dry eyes as well as drinking alcohol. Maybe it is just happen to somebody that their eyes twitching when they draw eye line. Or it may caused by allergies. Or If the eyeliner has some components that can cause allergies to your eyelids, it will cause eye twitches. So, if you feel OK to use your eyeliner, you needn't worry about it.
Well,yes, it is true. for your situation, I have to say that your eyes are infected by the eyeliners. As we know that eyeliners are made of chemicals. By wearing them, they can make your eyes be in the risk of infection. In that way, it can make your eyes to be pink eyes. As we know that pink eyes is an infection of the eye or eyes which can lead to redness, itching, irritation, and a characteristic creamy discharge in your eyes. Anyway, when you use the eyeliners, they can carry many allergies which can lead to infection to your eyes. So you should not always wear eyeliners. Also, making them not be with allergies is also important. For your situation, you can drop some eye drops in your eyes, and it can relieve your symptom.