Permanent Damage to Face From Chemical Peel? (Picture Attached)

The beard hairline is naturally irregular and normally zig-zags.  The beauty of chemical peels is that they don't cause hair loss.  The 15% TCA chemical is very mild.  So mild that it is considered to be a no down time procedure.  This chemical peel did not cause any change to your beard.  Given that you believe something different, I would strongly advise you against getting further chemical peels or for that matter any cosmetic procedures.  

You are developing a post inflammatory hyperpigmentation.  Treatment for this type of problem includes the use of hydroquinone 4 to 8 %, Kojic acid, Retin-A, Topical steroid creams.  You can expect it to take up to 10 weeks for the pigmentation to clear. 
Also available from a compounding pharmacy is Klingman's formula which is a mixture of all of the above chemicals.

I doubt that 15% TCA would have caused any of these problems. This is a very light peel. Make sure that you use sunscreen daily.  

You have the same pattern when you compare your before and after pictures. TCA 15% does not penetrate deep to cause the hair shafts.