Is this burned or will it heal after I applied TCA 40% peel? (Photos)

You demonstrate the typical post treatment redness and peeling of a chemical peel.  Once the scabs have come away apply regular moisturizer on a daily basis. Keep out of the sun for 6 months!  The areas will remain redder than the rest of your face for about 1 year.
If you have any ongoing concerns it is always best to return to your PS for reassurance.

TCA peels are self neutralising - once frost its all over red rover. White areas are protein coagulation. The pictures reveal redness and brown edges. We do not know the real depth of the peel due to your application. Additionally more info needed- ie. acetone scrub, technique? base of TCA? ph of compounded solution? Skin hx??? etc..etc.. for now,  use sunscreen, if possible see a dermatologist for GENTLE Q switching and titrated HQ. Agreed, in your skin type, about 6-12 months to heal. In darker skin types this can take 2-4 years to heal. All the best, Dr Davin S Lim. Brisbane.