How to know if I need braces for this underbite?

Underbites. Underbites do not self correct. Please see a bite specialist, an orthodontist, for evaluation. At an Orthodontist's office initial examinations are usually free or modest cost. Please call for an examination. You'll be glad you did.
Orthodontist. Only an orthodontist will decide that for you. Please get a checkup by an orthodontist.
Consultation. A consultation with a local orthodontist is the only way you will know if orthodontics alone will correct your malocclusion, or if a combination of orthodontics and surgery is necessary.
If you want it fixed. As an adult the only way to correct your bite is with braces. It may be possible to use removable or fixed braces to make the correction.
See orthodontist. only an evaluation from a professional that can see your teeth and bite will really be able to assess.
Does it bother you? If it does not bother you, then no, you don't need braces. If you don't like how it looks, or if it interferes with function then see an orthodontist and find out what needs to be done to change things.