I would like my lips not to curl inwards when I smile and I would also like the corners turned up. Any advice? (Photos)

If you have not seen satisfactory results with Botox treatments, your best bet may be a surgical lip lift. This procedure uses a tiny incision under the base of the nose to shorten the philtrum and create lift to the upper lip. The procedure increases mucosal show and reveals more teeth when you smile. It would also turn up the corners of your mouth. Choose a board-certified plastic surgeon for your procedure who has performed many lip lifts. This will ensure an optimal outcome. 

There are surgical and non-surgical approaches to lip augmentation. Non-surgical approaches include botox (slight lift, reducing gum show) and filler (volume restoration). Surgically, you can have two separate incisions under the nose (italian), one incision under the nose (bull horn), one incision at the red/white upper lip junction (gull wing) or two separate incision at the corners, or a combination, depending on your desired look and anatomy. My preferred surgical technique is called the Elelyft, which is a version of the bullhorn approach. In your situation, I would definitely recommend visiting a cosmetic dentist prior to any lip surgery. Consult with an experienced lip specialist for a complete range of options that are appropriate for your situation.
Gary Linkov, MD
Lip Specialist / RealSelf Lip Lift Medical Reviewer
Manhattan

this is more of an anatomy issue you could have a lip lift and/or surgery to fix your teeth and the bone structure but all of those are more expensive and more healing.  Fillers and botox can be used as well and longer term fillers used like voluma.  always use a lip plumper too (see link). Best, Dr. Emer.