The right answer depends on many factors that only your dentist will be able to discuss with you. Yes, you could have composite or porcelain veneers, the "no-prep" kind, where little or no reduction is done to your teeth, but this may not address your concern of a "gummy smile". Most likely, you would need a minor surgical procedure known as a "gum lift" where the gum-line is raised a few millimeters, and in doing so it diminishes the gummy smile look, making the teeth look longer and the gum shorter. After the gum lift, it may be necessary to correct the shape of your teeth with veneers. At 16 years old, you're still a little young to have traditional veneers, but I would strongly suggest you consult with your dentist and a periodontist to see what alternatives are available to you.
A "painful bulge" on the gum around a tooth is something that should be addressed prior to placing a crown. A gingivectomy, while sometimes necessary before completing a crown procedure, may not be what's needed in this particular case.
