Options To Correct a Crooked Mouth?

Most of us have more muscle tone on one side vs. the other. As you said, no one notices these unless they are pointed out. Leave it alone--you have a pretty smile and that is what counts.

You have a subtle problem that appears fairly "real."  That is to say that the right side of your mouth at rest is is pulled more than the left, which is shifting your philtrum (central part of your upper lip).  The problem fortunately seems to disappear with aggressive smiling.  You are most likely habitually activating the right corner of your mouth at rest, but you may not be aware of it.  Sometimes, this sort of appearance may be due to facial weakness on one side as one might get when recovering from Bell's palsy (or temporary paralysis of the facial nerve).  However, it sounds like this has been a lifelong problem.  To correct the habit of shifting your mouth to the right, you may want to consider biofeedback therapy with a trained therapist who specializes in facial weakness or paralysis.  Alternatively, very careful administration of Botox or Dysport on the overactive right side of your face may balance your closed lip posture in repose.  If this problem is truly bothersome, then I would suggest seeing a board-certified plastic surgeon with expertise in facial paralysis for a more accurate recommendation.

There are options to help improve and lift the corner of the mouth to help achieve symmetry.  However, you need to consult with a board certified specialist who can best evaluate and assist you with this.