Yes, the amount of swelling you are showing can happen with some patients (not all) and is nothing to be worried about. It will come down within a few days, up to a week. The numb feeling in your lips is most likely from a combination of the swelling and any possible lidocaine in the filler that was used, so don't worry about that either. Use ice packs to help with the swelling and stay hydrated!
Invisalign and braces are simply tools we use in orthodontics to achieve a functional, beautiful smile. As such, not every tool is right for every person. Your dentist will do a full evaluation of your dental needs, your lifestyle, your desires and goals and your age, to come up with a treatment plan that is custom-tailored to you. I don't believe in a one-size-fits-all approach to orthodontics, because no two patients are exactly the same.