antibiotic help peeling lip (ec)

Hi everyone i am new to this forum and I had exfoltive cheilitis for over 5 years.all I have been doing is constantly keep my lips moisturized with different lip balms.recently I have went to the gp about my lip as it was swollen and had yellowish crust(mainly on the lower lip).the doctor suggested that I should try antibiotics in order to get the infection treated first and so far I had been using it for 2 days. the results are confusing me because my lip doesn't dry as fast and crusty yellowish skin isn't visible but i don't know if I should keep using these antibiotic.I have found in different websites that antibiotic doesn't cure ec, so should i continue using them for 5 days more or stop?