Can you neutralize a chemical peel at home with water/facial cleanser? Or should one use baking soda?

It's not uncommon to experience some changes in your skin after a glycolic acid peel, especially one as strong as 50%. Typically, glycolic peels can cause temporary redness, peeling, and dryness as they exfoliate the outer layers of skin. However, the symptoms you're describing—such as i...

You don't necessarily have to see full blown peeling to have good results.  The texture and pigmentation can be improved even without significant peeling.  It is usually takes several peels to see the overall beneficial results of the peels and improve your skin.

Deep chemical peels are pretty uncommon these days just for the reasons that you are describing.  You can get red and stay red for months.  Proper wound care and sunscreens are necessary as this can take a long time to go away.  Best, Dr. Green