If the makeup you have has come in contact with your eye before you got the stye then you do need to throw the makeup away because it could contain bacteria that caused the current stye and you could get infected with another stye if you use the same makeup.
Throw the makeup away and get some fresh makeup.
While you have a stye do not wear any eye makeup and avoid touching the stye except to put ointment or treat it another way.
A good home remedy that works to get rid of styes is to use a warm tea bag that will act as a compress on the stye.
Place a warm tea bag over the stye and let it sit for around 10 to 15 minutes. You may have to do this a few times a day before the stye will go away but it will eventually go away.