Good that you've got some tests planned. Given that diet was restricted hopefully they'll agree to test your ferritin, B12 and vitamin D as well.
I'm not remotely qualified in this area, so these suggestions are just from my own experience (although I've never had the dents). I've previously lost huge amounts of weight fast due to severe anxiety, and gone through an endless perimenopause.
I'd take a fish oil supplement. Quality really matters, this is a very good brand:
igennus.com/products/vegepa-high-strength-epa-fish-oil-with-gla-omega-3-omega-6-60-softgels
That one has evening primrose as well, which can be beneficial.
Also, vitamin D plus K, and vitamin C.
If you could go to a really good professional dermaplanner and explain how your skin responds to hair removal, that could be a way forward, but I'd want someone who specialises in it and is recommended.
I don't know the Avene cream you're using, but I've been using this on my face:
www.boots.com/la-roche-posay-cicaplast-hands-50ml-10237661
Seems odd as it's sold as a hand cream, but it's so soothing, bland and not sticky after the first couple of minutes.
Rosehip oil is another really nourishing product to try:
www.boots.com/the-ordinary-100-organic-cold-pressed-rose-hip-seed-oil-10267770
(Don't know how much you can spend.)