When I smile, the center of my top lip pulls down while the rest pulls up.

Hi.  You need to post a pic without smiling and one with smiling for us to see.  But from the sounds of it, you would need a small amount of Botox to the top lip laterally to decrease the elevation and thinning of the tip lip laterally as well as fillers to the lateral top lip leaving the central lip untouched so that they blend better and balance better.  But without a few pictures its hard to tell.  Just know that Botox does have a role in lip beautification and its not just fillers

Hello,

You can obtain a balanced appearance in the lips with the use of hyaluronic acid based lip fillers towards the center towards the corners of the lips and the Botox/Dysport injections to the upper part of your lips which weakens over time, giving it a lifted appearance. 

I recommend booking an in-person consultation with a certified cosmetic facial cosmetic surgeon. When you are exploring the options of a facial procedure, make sure that you also explore the right type of cosmetic surgeon to perform your procedure. A facial plastic surgeon is a cosmetic doctor that is an expert strictly in the head and neck.