Of course you can tell your therapist you don't want meds.
I will say, though, that I resisted taking meds for years and years despite recurrent depressive episodes, and, once I did, it was life-changing. It gave me a lot more strength to confront a lot of emotional things I had been avoiding that would otherwise be overwhelming.
Which is just to say that I don't think it's either/or. It's not like taking meds is *instead* of dealing with the deeper stuff. For me it just helped me contain my anxiety enough to actually look at and handle the deeper stuff.
Like you, without meds I could outwardly look normal and was "functioning." But I wanted to do a lot more in my life than just function. Meds helped me do that, but it still also required a whole heck of a lot of work in therapy as well.