I'm not sure what you mean by filing "independently." You can always file your own tax return, separate from your parents' tax return. Your income cannot be reported on your parents' tax return. If you made $13,850 or more you must file your own tax return. (There are circumstances in which you must file even if you made less than $13,850.) The question is whether you have to check the box on your tax return that says that someone can claim you as a dependent.
Based on what you wrote, if you lived with your parents for more than half the year, they can claim you as a dependent. Time that you were away at college counts as living with your parents. If they can claim you, you must check the box on your tax return. It doesn't matter whether they actually do claim you. The question is whether someone can claim you.
Your parents cannot see your tax return under any circumstances without your permission, whether or not they can or do claim you as a dependent.
