4 weeks negative 6 weeks positive, possible?

Sounds like you have all the symptoms. Sometimes it takes a while for the hcg hormone to build up in your body. I didn't test until I was a week late for my period and It was a faint positive. I waited because I didnt think i was pregnant, just thought i was late. I'm still pregnant (8 weeks)! I had very sore boobs, was moody, and could smell everything a mile away. You have more symptoms than I did, sounds like a good sign! You are probably just testing too early. Good luck to you!