You bring up several good points.  With TCA peels or almost any procedure, there is the procedure itself and then there's what comes afterwards.  When there's a complication, sometimes it's the procedure and sometimes it's the post care that the problem.  It sounds to me like the peel went fine but now you're not healing well and often the culprit is the products you are using afterwards which are creating an irritant or allergic reaction.  I'm wondering if that's the problem.  In my opinion, hydroquinone 4% is almost always too irritating to use on eyelid skin.  I would recommend stopping it for now. While you are waiting to see your dermatologist again, try just very bland Vanicream or even vaseline.

Finding a good dermatologist to help you now is key. You didn't mention if your doctor is a board certified dermatologist.   I think you'll need one to help you manage this problem.   I hope this helps.  Dr. I