The only interference would be taking the supplement at the same time -- in general, take the thyroid medication in the am (at least 30min before breakfast) and supplements with lunch or in evening -- that is the easiest way to avoid interference w/ absorption.
what you describe are all symptoms of hypothyroidism. for most of us its corrected with the right dose of meds. maybe this is what you should be thinking about more than trying to cure all these 'individual symptoms'. 50 is a low dosage. if you have been diagnosed with hypo, i suggest you return to your dr ,tell your symptoms and get bloods checked to see if you need to up your medication.
Do you have a Trader Joe's near you? They make an excellent Women's vitamin for Hair, Skin & Nails.
Do you have any recommendations for supplements that will alleviate some of the problems associated with hypothyrodism (i.e. dry hair and nails, hair loss)? Thank you.