What makes you think mewing would be bad for you? I have never heard of anyone suffering from any negative side effects due to mewing. Otherwise, I can not say for sure what your specific issues are, since I myself yet have much to learn. Something I can say however: I would never think you where in need of surgery. In my opinion, you look pretty handsome already. Stick to mewing, strive to be the best you and I am sure you will do fine!

honestly speaking, you're pretty handsome and there's absolutely  no need for surgery. you've got a good jawline just chew more equally on both sides.

You have what is called a hypodivergent facial type, otherwise known as brachyfacial. A deep bite with no overjet is standard on this skull formation. The maxilla is in a good position UPWARDS but otherwise in a bad position backwards. 

Mewing may help lengthen your lower third which IMO is what will benefit you the most since your chin is already strong. It would clockwise rotate your mandible which can add length. In your case you don't need facial shortening since your face is already short. This is why I said you may benefit from some lengthening as your lower third is equally as long as your middle third. That will give you a longer more masculine philtrum. But you won't look like an ape since your lips may get fuller to balance it out. 

In turn this may help your cheekbones pop out more and your lips look less sunken in. Your chin will stay strong, but your face will be more balanced. Maybe your midface ratio may shorten a bit but probably not by a lot.

Because your maxillary height is decent but your maxilla is back a bit, pulling your maxilla down by engaging your posterior third will help move your teeth forward. So the maxilla would move down in order to move forward. This will counterclockwise rotate your maxilla which will allow your bite to open more as opposed to being so deep. So in your case, maxillary downward movement will allow your maxilla to go forward a bit.