Obagi Radiance (Blue Peel) no TCA/ What can I do about dark, flaky, dry and irritated areas? (Photo)

Thank you for your question and for submitting your photos.  I'm sorry to hear that you are experiencing complications from your Obagi Radiance Peel.  It's difficult to make an exact diagnosis without assessing you in-person, but based on your photos, you appear to have postinflammatory hyperpigmentation, or PIH.  PIH can occur after any type of inflammation of the skin, such as rashes, acne, injury, or as in this case, chemical peels and lasers.  I find this is especially a problem for patients with darker skin types, particularly when they were not adequately prepared for their peels with good skincare and/or were not provided with good post-peel skincare instructions.  
The good news is that this type of pigment can be treated, however it is very difficult, and will take a long time.  The first step is strict sun protection - the stubborn pigment on your face is very sensitive to sunlight, and every time you go outside without good sunscreen the pigment will get darker and will become more persistent.  I would suggest that you start using a sunscreen absolutely every single day with no exceptions.  I would recommend a product with an SPF of 45 or more, and containing zinc oxide or titanium dioxide for best protection.  I would also recommend reapplying it throughout the day, every 2 hours, particularly in you are going to be outside.  You also appear to still have some residual inflammation in your skin, which may need to be treated with a prescription strength steroid cream.  In addition, a prescription-strength skin bleaching regimen should help start fading the pigment as well.  I would recommend that you see a board-certified dermatologist with extensive experience in chemical peels to discuss your treatment options.

PIH after chemical peels need topical treatment and I recommend Melarase as a daily regimen along with an oral PIH Relief Complex formula called Scler-X.H Karamanoukian MD FACS