Skin arround mouth and chin are very sensitive. If you are using acids and actives there then it will worsen this situation and make the skin there very dry and flaky. Otherwise if your skin’s moistur barrier is already damaged then it might be the reason for this dryness.
I would suggest you to stop all type of actives like retinol or acids like Vitamin C, AHA/BHA. Cleanse with mild face wash and use hydrating toners and essence. Get a intensive moisturiser with ceramide and niacinamide. Stay away from hyaluronic acids for now. Never forget your sunscreen with high spf, apply and re-apply it throughout the day even when you are staying home.