Hydroquinone cream should be used only after consultation with a dermatologist and as per prescription. I hope it is what you did. The best person to consult now is your dermatologist. The skin becomes extra sensitive after the use of this chemical and exposure to the sun should be avoided. Skin darkens, despite using this skin lightening cream because of the reaction to the ultraviolet rays. Remember, the skin becomes extra sensitive.
Hyperpigmentation could be due to a hormonal imbalance. You need to see a doctor who will run a few tests to determine the exact cause.
Meanwhile, try some home remedies, but before that allow the skin around your mouth to heal. Apply pure aloe vera gel, taken from a real plant, not from a jar. This has a soothing effect and will improve the skin. After about a week try the following home remedies, but note that if the problem is hormonal, the skin colour will not change.
1. Mix aloe vera gel with lemon juice and apply on the affected area. Leave on for 15-20 minutes and wash with normal water. Can be used daily, but avoid sunlight.
2. Mix sandalwood powder and honey and gently massage the area around your mouth. Do this on alternate days
3. Powder massor dal and moong dal. Take equal quantities of the two, mix with rose water and use as a scrub. use once every 15 days
4. Soak cotton in pure milk (unboiled) and wipe your face with it. The lactic acid in milk has excellent skin lightening properties
5. Apply a mix of curd, besan (gram flour), haldi (turmeric), sandalwood and honey on your face. Use it as a face pack. Let it dry and then wash with normal water.
6. Keep your skin moisturised and use one suitable for your skin type
7. Use an umbrella and wear sunscreen lotion every time you go outdoors
8. Stay hydrated; make sure you are not constipated and eat a healthy diet - lots of fresh fruits and vegetables
9. Rub vegetables and fruits on the affected area. Whatever you can find in the kitchen. Potatoes, tomatoes, banana, papaya, orange juice, crushed apples etc.