Why don’t my top teeth show when I smile? How can I fix this? (Photos)

Its a little tough to answer this without an actual clinical examination and pictures with the lips retracted to assess the length of your teeth.
However, if there is a tooth length issue, porcelain veneers is a great way to increase the length. Alternately lip repositioning to increase the display of upper front teeth might also be a good option if tooth length is adequate.

Judging from your smile, I would say using porcelain veneers would be your best solution on 8 teeth to give you the smile that you've dreamed about.

Hi,
Thank you for the question and details explaining the situation. 
Your question brings up a few good areas to address. Has your smile always pulled more on one side, or has that developed over time? Also, your TMJ issues need to be looked into and your bite should be checked to see if everything is balanced from the orthodontic work. 
It looks as if your teeth have been stripped in between, most likely during the Invisalign. This makes the teeth look more square and unnatural. That being said, it makes you and excellent candidate for porcelain veneers. With veneers, you can conservatively lengthen, whiten, and balance the symmetry of your teeth. Based on the pictured you attached, I would recommend a minimum of 6-8 veneers. 
Most important decision is to seek out an expert who has successfully treated cases similar to yours!