Would Botox in the levator labii superioris alaeque nasi benefit me?

I have this natural snarl on one side of my face that is helped with filler when injected in the pyriform fossa. However it never seems to last very long. Naturally, i look annoyed even when im not and the muscle there naturally lifts up that side of my top lip as seen in the pictures. Even when closing my mouth, the side iof my lip is very slightly open. Would botox help in that muscle? Would it drop my lip down a little and smooth the wrinkle thats also there? The wrinkle goes all the way down to the side of my mouth. Please let me know what options i have. This is genetic as my dad also has the same. When i do get filler in the pyriform fossa it lifts my mouth and generally i look happier. Can this be acheived with botox?