Gradually changing your wardrobe to be more modest seems like the right way to go about it for someone in your situation, rather than making a drastic change. Also, you can still use Western style clothing provided it is modest enough. Unfortunately a lot of Western converts get sucked into this notion that they *need* to wear Pakistani or Arab ethnic clothing to be considered a "real" Muslim. There is a blog you can Google featuring the diversity of modern Muslim female dress, worldwide. It is called "Hijabs High." Different styles, and yes, even different amounts of coverage.
Trying to please everyone and wearing 2 different identities (1 in private, 1 for your family/friends) is an exhausting way to live. You're an adult and your family should respect your decisions about what kind of life you want to live. Gradual changes are easier to accept than sudden ones. I really respect people who are able to make that change into a new religious identity suddenly, but I have seen it with my own eyes that it often isn't good for a person to jump right into superficial aspects like appearances, when they are still taking spiritual baby steps. Faith is a journey which takes many years.
P.S.: I think this obsession people have with women and what they do or do not wear is spiritually unhealthy, it is as if hijab has become the only measure of a woman's piety.