Summarize:

Home remedies may not help with dark underarms if you're suffering from a condition known as acanthosis nigricans, a skin disorder that results in velvety, light-brown-to-black markings in areas that include the armpits.  This condition can occur as a result of obesity or an endocrine (glandular) disorder. It is frequently found in people with diabetes or a tendency towards diabetes and is most common among people of African descent.    Other possible causes of acanthosis nigricans include Addison's disease, pituitary gland disorders, growth hormone therapy, hypothyroidism or the use of oral contraceptives. If your condition is diabetes related, modifying your diet to restrict starches and sugars may help. If oral contraceptives are at the source of your skin condition, you can try switching to a different form of birth control to see if the condition improves once the medication is stopped. Retin-A, 20% urea, alpha hydroxyacids, and salicylic acid prescriptions may help, but they've been found to be only minimally effective.   The most widely used ingredient in skin lighteners sold in the U.S. is hydroquinone, which is regulated by the FDA. Dermatologists can write prescriptions for lighteners that contain up to 4% hydroquinone.   Over-the-counter skin lighteners can contain no more than 2% hydroquinone.  Always check with your doctor before using a product that contains hydroquinone. Use skin lighteners sold by trusted brands.  Although the FDA banned the use of mercury in skin lightening products in the U.S. in 1990, lightening creams that contain this toxic metal have been found here. These products were manufactured in other countries but sold in stores in the U.S., so read labels very carefully when shopping for this product. All women, but especially those with dark skin run the risk of hyperpigmentation (skin darkening) when they use electrolysis for hair removal.    If you've been having electrolysis treatments to remove the underarm hair, stopping the treatment should stop more discoloration from occurring.
Check with your doctor. Change your diet. Stop taking the pill. Get a prescription. Stop electrolysis.