This is your new life. She's gone, and the best way to stick it to her is by being happy and making yourself the best person you can be. This is your chance from a fresh start. You've already gone 3 weeks without smoking why stop now. Not sleeping sucks but there's plenty of other options for you to try instead of smokeing. Try gravol, i know that helps some people.
Your probably in a better position than a lot of people. Your not hung up on your ex, be happy that you don't want her back and that you can just move on. It's completely normal to get mad at an ex. But there is a point where you just have to put your anger behind you because that's in the past. If you don't want to think about her then just remind yourself that she isn't worth the time or energy, easier said than done I know.
If you can't get her out of your head now just give it time and you'll find yourself thinking about her less and less