if you could get serum ferritin, serum zinc, serum magnesium, serum copper and serum selenium looked at, in addition to an updated serum 25(OH)vitaminD3 result, that could help. a serum vit b12 level couldn't hurt either.
cutting out gluten and dairy can help mitigate ongoing depletion, but in the best case scenario all that really does is help the rest of your diet meet daily requirements. assuming that diet is sufficiently nutrient-dense, of course.
gluten free diet CAN'T necessarily facilitate replacement of chronically depleted nutrients.
I hadn't heard of biotin being a major nutrient of concern in ms, but I can tell you for sure that since I got sick and started working on identifying and correcting nutrition issues, that my hair, nails, eyes and skin have all improved.
so, testing is smart. and then possibly a short term therapeutic supplement regimen to kick things back into gear
and a review of day to day diet to see if any food/fluid selections would benefit from some tweaking
would be smart to have everything optimized for sure!
I am sure there are others here with endocrine expertise that could recommend other specific tests - other than that my regimen thread (link below) has a ton of detail on nutrient testing, including target levels to aim for within the various normal ranges out there.
hope that helps!