Hi H
Styes/chalazions or lumps in the eyelids due to blocked glands can be drained when they persist despite conservative treatment like hot compresses and antibiotic eyedrops/ointments, and if they are large enough to be bothersome.
Large styes may cause not only cosmetic issues, if they are in the centre of the upper eyelid they may even press on the cornea and cause temporary visual blurring.
Although they may go away by themselves eventually, sometimes this could take months.
So if you have already had the stye for 3 weeks, and it is bothering you and not getting smaller, you can consider going to see an eye doctor to have it drained. Otherwise, you could continue with conservative measures first also.