How can I get rid of this dark discoloration around my lips and on my lips? (photos)

That is not normal.  You need to see a Dermatologist.  This is not a simple matter of throwing around chemicals. Get a real opinion.

Treatment with prescription steroid cream will reduce irritation .Thisxcan be combined with bleaching cream to lighten the dark area.Do not chew gum ,use sucking candies and change your toothpaste to sensory r.This Amy be allergic contact dermatitis.

I would suggest discussing your concerns with a dermatologist. Should you have the habit of licking your lips, please stop. You may need a series of chemical peels and treatment with Retin A and Hydroquinones to get your best results.

The skin above your upper lips are hyperpigmented and irritated.  I would suggest you use a hydrocortisone cream for a very short time to reduce the irritation and then a bleaching cream with Retin-A to remove the pigmentation.  Chemical peels in this area are very effective. Best, Dr. Green

I would see a dermatologist for this. You need to start retin A and hydroquinones. Chemical peels might help too. With your dark skin type I don't recommend any energy based treatments.