congrats on 30 days clean! that's so good!
if you trust her then go for it! it feels so much better to tell someone, like a mahoosive weight has been lifted off your shoulders
you could tell her in person after your lesson or arrange to see her in a break, or you could email her or pass her an envelope with a note in and write on it 'to be opened in private, this is confidential' or something? there's plenty of ways you could tell her
i wish you the best of luck and this is so brave!
*hugs* <3