Follow-up question: 2 weeks post laser hair removal burns. Will these eventually fade over time? Will Biafine help? (photos)

Thank you for your question and posting pictures.  It looks and sounds like you might have Post Inflammatory Hyperpigmentation (PIH).  You can start by looking for prescription strength 4% Hydroquinone (HQ) to reduce the pigment.  Do not buy it over the counter or off the internet.  Laws vary by state.  In Texas, physicians can prescribe and dispense in office.  We have been very successful using the PicoSure laser with the FOCUS and / or Flat Lenses eliminating hyperpigmentation with a series of treatments.  
FOCUS lens treatments have the extra benefit of reducing the underlying scar tissue.  This is one of our go to treatments for patients older than 40 and worried about the signs of aging.  This laser is safe for all skin types.  Start with sunscreen every day!  Once you have treated your hyperpigmentation to your satisfaction, you will probably need a follow treatment every 6 to 12 months depending your level of re-pigmentation.  Best of luck.

So sorry this happened!  "Burns" and the resulting hyperpigmentation are the most common significant side effect from laser hair removal.   They result from multiple factors including your skin type, sun exposure, the type of laser, and the laser settings.  
Typically these will fade with time, but often take months.  I recommend continuing to followup regularly with your provider.  There are things they can do to help such as daily use of prescription 4% hydroquinone cream.