I Have Extremely Chapped Lips For 3 Months. My Doctor

I have extremely chapped lips for 3 months. My doctor prescribed Mupirocin Ointment, 2%. I have used it for 3 days now. My lips are still very chapped. I stopped using the ointment for 6 hours now. Does the Mupirocin dry out lips further?

I have also been diagnosed with HS-1 and just had my first outbreak last week. That is healing well (was not on my lips). I am taking Valtrex presently.