Will these scars heal? I’ve had had TCA cross done on these 2 scars about a week ago. (photo)

Hi,
Yes they should heal fine. It is just too early to assess only 1 week after your peel. It usually takes several weeks for the skin to regenerate and then several months (up to 6 months) for the skin/scar to mature depending on the depth. So be patient and you should see improvements weekly, not daily!
Dr. Hamrah

TCA CROSS healing will depend on 1. The concentration of TCA 2. The formulation of the base - alcohol vs hydrous (water) 3. The coats 4. Your skin healing- 5. The site 6. Any comorbities like smoking, exercise and infection 7. The area treated - small e.g.. Ice pick vs large e.g. confluent narrow box car scars. 8. patient compliance in regards to wound care guide
Now that you know the factors one can gauge healing. OK, so for this area and extent I would expect healing by day 8. Your post op instructions should include wound care. Respecting your plastics or dermatologist own post op instructions, mine are- 1. wash bd with H20 and or Cetaphil / QV face wash. No sunscreen till wound completely heal. 2. WSP or QV Intensive 3-4 times a day till healed. If large areas treated I cover with oral and or topical Abs. 3. Apply for 7 days. NO scabs, - keep wound moist. If it scabs it scars! 4. SPF any day 8- 10 once complete healing has been achieved. 
If you have any doubt, go back to your specialist. As a general rule, specialist will make it CRYSTAL clear to the patients in the context of wound care. Vital to understand that a procedure is one thing, but 50% of the end results will be dependent on post op wound care and healing. I hope this gives insight in regard to how we think when it comes to factors that may determine your heal times and how we approach wound care.