How can I treat hyperpigmentation spots on my leg due to a chemical peeling burn from July?

Unfortunately time is not on your side.  This will take some patience.
Skin lightening creams are possible but can also result in hypopigmentation - thus be careful and take advice from a dermatologist with experience.

There may not be any way to completely resolve this in a month.   Hyperpigmentation on the legs is slow to resolve.   Legs do not heal like other areas of the body.  Depending on the location and type of pigmentation, topicals (like you are using), light chemical peels or laser treatments could be effective.  However, it should be evaluated in person by a Board-Certified physician in Dermatology or Plastic surgery who specializes in cosmetic treatments.  Beware of medspa type facilities, and definately don't try to treat it with products from online.  If you can't get it resolved, there are some great cover up stage make ups that can be found, like Dermablend, that can be matched to your skin tone. Best of luck.

Hi boba90 and thanks for your question.  I'm sorry to hear about you experience but by far the most important thing for you to do would be to get evaluated by a properly trained provider that can examine your legs and give you proper treatment options.  It might be best to try to conceal the areas for now as sometimes rushing into a treatment prior to a major event is not the best idea, but you should get examined first.