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Hello and thank you for your question.
Most styes do not develop drainage or discharge. They are usually a closed collection of fluid that resolves over the course of 2-3 weeks. Warm compresses can facilitate it's resolution.
Since you have discharge, it seems that your stye is infected. You should see a doctor as soon as possible for antibiotics. Depending on the severity, you may just need eye drops or perhaps oral antibiotics.
I hope this is helpful. I wish you the best!
Hello. I just wanted to follow up with you. I hope you have been able to see a doctor and that all is well.