i have acne prone skin and lately i have been facing a problem of extremly dry skin around my nose and under the lips on chin area

First and foremost, it's important to keep in mind that everyone's skin is different and will require different care. With that said, here are five tips for keeping your acne-prone skin hydrated:

Drink plenty of water.
Avoid alcohol and caffeine.
Use a gentle cleanser that doesn't contain any harsh chemicals or sulfates.
Apply a moisturizer (preferably one that contains SPF) every day, even if you don't feel like your skin is dry.
Consider using a humidifier to add moisture to the air in your home or office.