What are these lines on the sides of my chin and what can I do to get rid of them? (Photo)

Hi Lola.  The lines are a natural part of your facial anatomy.  It's likely an issue that can be camouflaged with dermal fillers, but it would be easier in person to know.  To see examples of others that have had injections for the chin, click on the link below.

These are actually an extention of your smile lines and are genetic. Filling them actually makes them look worse in my opinion.  Often we are doing fractional laser or radiofrequency to tighten them or chin contouring deep on bone with fillers to give this area a new shape. I suggest seeing a facial rejuvenation expert. If you really desire fillers, restylane silk or belotero work well because they can be injected very superficially to soften but not fill. Best, Dr. Emer.

Many lines exist around the chin area. Some of them are static( present all the time), others dynamic showing only during smiling.A combination of fillers and botox is usually succesful in taking care of this problem. 

I recommend Vivace Microneedling to tighten and rejuvenate. You will need 3 treatments and after if there is no improvement then fillers!