Well, in all honesty, I feel that you should continue to study but also obtain an internship at a company that would help you understand more about the industry. That way, you would still have your degree, and also have a leg up on everyone else whom is trying to become a freelance illustrator. Being an intern will put you in contact, even if indirectly, with many people or businesses that could help you with your career.
I'm sure your mom is only trying to harden you to life's cruelties. Inside, she's probably cautiously delighted that you are making such decisions regarding your future. Parents tend to be overprotective of their children and do not want to see them struggle or be hurt. It's rather sweet of her, in an odd sort of way, that she has been trying to steer you in a different direction.
If you continue your studies and opt to take on an internship at the same time, I believe your mom will be satisfied to a small degree that you are both willing to abide by her advice, but wanting to break out on your own. Best of luck in your decision!!!