Hi Naomi, welcome to DermaTalk. The picture is not that clear, if possible post a clear picture in a normal daylight without modification. So, u r are talking about the round black spot near mouth or are there other multiple spots too. The one near on the mouth does resemble FDE (Fixed Drug Eruption), but any way you said you had herpes outbreak on the exact same location, is that right? So lets assume its post inflammatory hyperpigmentation.
So what topical medications have you applied beside hydroquinone?
There are several topical depigmenting products like Hydroquinone (HQ), retinoids, kojic acid, arbutin, azelaic acid and licorice extract etc. that can be applied alone or in combination to achieve good results. Combination works better than single. If low strength is not working good one can shift to high strength, but remember, if the pigmentation is beyond epidermis (ie. deeper to the dermis) these topical agents will not response well. You may need mid-to-high potency chemical peels to get it removed.
So if you are only using HQ then go for combination products.
You may go this way first:
[A] hydroquinone+tretinoin+steroid
[B] Kojic acid+arbutin+licorice extract
You may apply these combination alternating A & B every night for 3-4 weeks and see if that works..I'm not sure about the brand names of this product in your country but these products are often combined this way.
REMEMBER: The most important part is to avoid sun, so always apply broadspectrum sunscreen on SPF 30+.
If nothing works chemical peel or lasers may be the other options.