If I opt for lip fillers, will they simultaneously address the wrinkles, or would I still require Botox separately?

Lip fillers are mainly used to add volume and enhance the shape of the lips, rather than directly targeting wrinkles around the mouth. If your main concern is addressing wrinkles, especially around the lips (such as smoker's lines), lip fillers may not provide the desired improvement.

Botox is the first option when it comes to treating wrinkles around the mouth. So a combination of lip fillers and Botox may be recommended to achieve comprehensive results, as in your case. Lip fillers can enhance lip volume, while Botox can address dynamic wrinkles around the mouth area.