Is It Possible for Me to Have Lingual Braces and Veneers at the Same Time?

It is best to have your orthodontic work fully completed or near completion.  Often times, restorations including veneers will turn out much better if you have straight teeth. I agree with the dentist get temporary bondings to fills in gaps while you are in orthodontic treatment.  

Also, we can definitely reshape your teeth.  We like to also try to do this at the end of ortho treatment  when the teeth are straight.  Your orthodontist will be able to determine if in fact your teeth are proportionately longer .  Usually teeth appear long because they are just hanging lower but when the orthodontist levels the teeth through orthodontics the tooth that the patient thought appeared long was in fact normal length. 

It sounds like you would like to have a great smile as fast and inconspicuously as possible!  If this is the case, it would be a great idea to ask these questions when you go in for a consultation so you'll know what you will be dealing with. But in general, you would have the braces done first to put the teeth in a favorable position for the veneers. As for your longer teeth, you may want to wait on filing them down, as the orthodontics may take care of this by moving them up. Make sure you have a good plan for how you want your cosmetic outcome to be BEFORE you start any dental work. Have you looked into Six Month Smiles orthodontics? It's an almost invisible way to have straighter teeth in much less time, as the name implies. All the best to you!

Congratulations for fixing your teeth-Consider doing braces but use the front kind and it will block what your teeth look like.  DO NOT do veneers until you have completed your orthodontic treatment(braces).  Make sure the orthodontist knows what bothers you-If you have decay, fix it-otherwise get through the braces and then get cosmetic dental care.  The orthodontist can refer you to a cosmetic dentist and they can work together to reshape and recontour as needed.  You won't be disappointed!