The reason for your underbite is probably due to an imbalance between your jaws, and/or the position and angulation of your teeth. From your photos, your lower jaw does seem more forward than your upper, and it is also off to the right hand side.
An imbalance of the jaws would be for e.g. the upper jaw being further back and the lower jaw being further forward. Kindly note that I am unable to give an accurate diagnosis based on your photos. A clinical assessment with X-rays is always ideal, in order for us to decide what is causing the underbite, is it the jaws/bone or is it more of the teeth.
I always tell my patients this - as orthodontists, we can move teeth, but we are unable to move the bone. In choosing which treatment option to go for, I would compare the pros and cons of each treatment.
If we choose to go for orthodontics or braces alone, then you will have to accept that there will be less change to your facial profile. We will move the teeth, close your gaps and attempt to give you a positive overlap of your upper front teeth, which is ideal. There are limitations, if the bone deviation is too much (for e.g. the lower jaw is too far forward), I may not be able to move the lower teeth in sufficiently to allow the upper teeth to be placed over them. Teeth will always need to stay in bone. For some people, they may be happy with this option.
The surgical option would correct the facial profile more and allow a more a dramatic change. You will still require braces or invisalign to align the teeth and guide the teeth into the ideal alignment and bite. Jaw surgery, as with any other surgery, does come with its risks, and the need for hospitalization for a few days depending on the complexity of the surgery and your recovery. The cost would also be more, but some of the surgical and hospitalization costs can be medisave deductible. This option will give you a more ideal result, then again the risk is also higher.
I would advise you to see an orthodontist for a consultation, and if he/she feels you would be more suited for jaw surgery, they can then refer you to see an oral maxillofacial surgeon, who can advise on the surgical aspect of the treatment. It would be best for you to know all your options, the pros and cons, and the cost of all the procedures, so that you have the knowledge to make a good decision on how to proceed.
All the best!
Dr Geraldine Lee