First of all, I'll explain this part "why not expand my face"
When thinking about an expansion, several things have to be taken into account, the positioning of your teeth, your jaw and your facial bones as a whole. Therefore, it is necessary to analyze the situation of your bite. Expanders are normally used in the case of an anterior crossbite, however,
In your case, you seem to have a class 3 underbite, not a crossbite, but I can't see your teeth, so I can't tell you if you also have some type of crossbite.
Now about pulling your jaw back and making you look ugly and resccesed. Dental braces will not make your jaw look like a mouth breather's jaw, it will make it look normal. You have to understand that continuing to have an underbite can cause several problems in the future, such as pain, asymmetries and facial deformities, in addition to not contributing aesthetically and that there is no homemade solution, you need professional help