Oh Lily, how awkward! I actually think you handled it really well. B f really shouldn't have shared that with his Mum but, coming from a close family who share stuff perhaps it was automatic and given his Mums profession he may have been seeking more understanding, which is good in a way.
His mother, on the other hand, was innapropriate and demonstrated a real lack of understanding. To tell youu to stop taking meds was completely out of ordder and to suggest she could sort you out is really wrong. It is inappropriate for a family member and on top of that is the language barrier.
You don't have to tell anyone anything you don't want to, including your Dad. If they ask, saying you don't feel comfortable discussing it or have been advised not to is fine. It wouldn't be a bad idea either to let bf know you won't feel comfortable telling him stuff if he takes it straight to his family.
I don't tell anyone anything about my mh issues except bare minimum to hb and some to my sister. I wish I could share more though as it leaves me very isolated with my feelings.