Nothing in the Bible tells us we ought to keep our faith private. It doesn’t exist. The only thing that comes close is the ”messianic secret” that Jesus counseled while He was still walking this earth. But even that was over when He rose from the dead.
Your faith ought to be something everyone knows about. There is no point to keeping praise for the Almighty in our heart. God demands and our lips declare the praise and glory of the Great King!
Don’t keep it to yourself.