When to use topicals on hyperpigmentation after 2nd degree burn

Hi,

I burned my hand from very hot milk approximately 2.5 months ago. The burn has healed completely without any kind of keloid or hypertrophic scar formation; however, the area is darker than my normal skin color (actually, the perimeter of the area is significantly darker than my normal skin color while the inside is about the same color as my normal skin with a slightly pink undertone.)  

For the first 3 weeks after the new skin formed, I used fresh aloe vera gel and a bandage to protect the scar from the sun, and after that I started to use silicone sheets for nearly 24 hrs a day (which also protect the area from the sun).  The hyperpigmentation stills seems to be diminishing, but I was wondering if silicone sheets is the best thing to use to speed up the process.  Ethnically, I am Indian, so my skin is dark.  The hyperpigmentation on my face due to mild acne responds extremely well to prescription retinoids (Tazorac), AHA, hydroquinone (Tri-Luma), and topical vitamin C serum.  My question is, can I / should I use these on the hyperpigmentation resulting from the burn? Would these (or another topical) be more effective at fading the hyperpigmentation than the silicone sheets?  If so, when can I start using these?  I don't want to aggravate the skin with something harsh like a retinoid or hydroquinone if the new skin is still forming/healing.

Thank you so, so much for taking the time to respond!

Divya