How can I amend my taxes? My parents were told they cannot claim me as a dependent this year because I made more than $5050, even though they pay for everything for me.

Yes, your parents can claim you as long as you are not providing over half of your own support, even if you made over $5,050, since you are 19 and a college student as long as you were a full time student for at least 5 months in the year. 

When you file your return you will just need to make sure you check that someone else can claim you as a dependent on their return so they're return is not rejected when they claim you.  Also, if you are paying for tuition with loans, they can enter your 1098-T on their return to claim an education credit if they qualify income wise and your school/education meets the criteria to claim the credit.  

The following criteria must be met to claim someone as a qualifying child:

• Your child (including adopted and foster children), your sibling, or a descendent of any of them.
• Age 18 or younger at the end of the tax year OR under 24 (and younger than you and your spouse) if they are a full-time student
• Lived with you for more than 6 months during the tax year
• They did not provide more than half of their own support (social security does not count)
• They did not file a joint return, unless it was to claim a refund