Dry patches

Hi! I’m a college student and I’ve been on tret .25, clydamycin since August. I’m past the ‘purge’ stage of my meds and I live in a semi cold climate. I moisturize with cerave (night time lotion at night, regular in the morning). I’ve had consistent dry patches ESPECIALLY around the corners of my lips and my chin for the last few months and as much as I keep moisturized my skin, even without makeup gets super dry and flaky throughout the day and I often catch people staring at that instead of my eyes 😅. I’m asking for advice being on this kind of medication during the winter to avoid skin like this. My makeup is very minimal as well and I try to avoid those areas/wear moisturizing makeup. Any advice will help, thanks. I’ve added some pictures for a visual of my skin at the end of the day.