Im a makeup artist and if a client blink a lot and and is uncomfortable with the mascara part then I either tell them to close their eyes and do their lashes while their eyes are closed or I let them to their lashes themselves. Cause no matter how skilled the makeup artist is it won't stop the client from blinking cause the eyes are sensitive and the eye are built to blink when things get to close to the eye in an attempt to prevent things for getting into the eye.
Yeah, I think there's a big difference between your mom and professionals. They can do it with your eyes wide open and closed without hurting you. They went to school for this so don't put off your passion out of that small fear. In fact, never put off anything you want to do because of fear of pain. It's usually the most painful experiences that gives us the most happiness at the end.