Is there another fix for rotated teeth that is faster than braces? (Photo)

After viewing your photos I feel that your doctor is correct.  Your bite is very compromised and full orthodontic treatment is the correct way to proceed. Your case may be able to be corrected in 18 months.  Seek out a board certified orthodontist for a consultation and you should be happy in the end.  Your smile will be both functional and aesthetic.  Good luck.  

Based on what I can see in your photo you appear to have a cross bite and this is unpredictable to fix by using cosmetic dental veneers or porcelain crowns. However, there are short term orthodontics or braces that can straighten your teeth on average in about 6 months. On of the more popular systems on the market is "six month smiles". If you do a google search on that you will find their website which provides more information. You can also find a provider near you or ask your dentist about it. 

The faster option is with porcelain veneers and porcelain crowns. This way we can change the layout of your teeth (we can change shape, size, color, etc), so they will look more aesthetic and you do not have to wait long time with braces.