I have burnt my face with a chemical peel, what should I do to repair my skin? (Photos)

Hi, Sorry that you have developed this. Use a gentle cleanser to wash your face. Usage of sunscreens plays an important role here to minimise post inflammatory hyperpigmentation. Consult an expert to deal your condition and to guide you properly. Best of luck.

First of all don't worry. It is unlikely that you have burnt yourself and caused longlasting harm. The peeling products that you used are all weak acids; that means they neutralise themselves as they go. You also neutralised them yourself. As you go on the peeling sequence it is normal for the peels to appear more aggressive as the layers of epidermis thin down to their normal depth. 
Use a very gentle healing product, such as aloe vera, or ideally one containing growth factors which really take the sting out of the peel. Don'rt forget sunblock whtever the weather.
In the future it might be wise to attend a professional to perform the treatment rather than doing a home peel.