What can be done to prevent my upper lip from being pushed forward as seen in the following photos? (Photo)

From your photos it is obvious that you have very narrow arches. It is also evident that your lower jaw is too far back and your upper front teeth are crowded out.Orthodontics moved your teeth but did not correct the orthopedic or airway problems.The DNA Appliance utilizes Epigenetic Orthodontics to grow your jaw bones orthopedically.  As your upper arch widens there will be more room for your front teeth to form normal arch.  This widening will allow your lower jaw and lip to come more forward and develop a pleasing profile.This will also serve to protect you from sleep apnea and snoring in the future as well as decrease risks of headaches, migraines and TMJ disorders.

I believe your lower jaw is too small. You need jaw surgery to advance the lower jaw. This will give your profile more harmony. 

The real problem appears to be that your lower jaw is retruded. You need what is called a neuromuscular dentist. Ideally, your palate(upper jaw) would be expanded with a functional removable appliance and then your lower jaw could actually be positioned more forward with restorations like crowns. I had this treatment myself and I'm very satisfied. But, it is imperative that you see a neuromuscular dentist for this treatment.