Hi there
it's been about a year since I hit puberty, so I know how it feels. I'm still in that phase. Like you I'm tall and skinny, and obviously now this is changing, and it's totally normal and fantastic. Of course it feels strange to suddenly have flesh where you didn't before, but try and enjoy it! You're becoming a woman, and that's something to be proud of. Bear in mind that you're no finished "developing" yet, in fact you've probably just started, so your body is just adjusting to this, and in the end you'll end up with the right proportions for your body type.
Don't be ashamed of your body, value it!
Hope this helps,
Skye