Are my facial changes due to my missing tooth? Will implants help? (photos)

Because you are young, it is more important for you to repair the bone and have implants placed for your missing lateral incisors.  As you grow older, the bone only becomes thinner and teeth more likely will shift.  That will change your profile even more.  Doing bridgework requires drilling down the adjacent teeth.  Bridgework will need to be redone after so many years, causing more damage to the adjacent teeth.
The road to implant supported restoration is a long one, perhaps a year, with great expense.  But it is worth it.

If you perform a bridge,will be something more faster and within a couple of days you will have the results you are looking for,there are good materials on the market like Zyrconia that is metal free,and can be a good option for you,the only inconvenience is that you will start to loose bone on the area where you lost teeth,vertical and horizontal,which is bone that will dissapear,and provably some day you will need it.
The best way to preserve the bone and to have that area like how it was is with Dental Implants that can be placed in just one visit,the only inconvenience is to wait at least 3 months for the osseointegration,and later on it will have a great result functional and cosmetic,for a long lasting term solution Dental Implants will be the best way to restore cases like yours,its worth the surgery and the waiting time,also search for a Dental Implant specialists so you will be in expert hands.