What I get out of your posts is totally different. I sense a woman who's crazy about you. After three months of dating she's writing things like ""I could live forever when you kiss me like you did last night" and though you posted "how should I play it?", the answer really was "Hey, DUDE! You're obviously doing all the right things! Just keep doing whatever you're doing"
And you must've, because you had some great dates with her since then, and when you felt ill, she offered to come over and make you dinner! Wow. That's great!
So when you turned down her offer, I think you really hurt her feelings.
And yeah, I think you sent her out a bad signal. And so maybe she is taking the incentive to get out first because she's afraid she's going to get hurt or maybe she thinks you've got a mean streak or aren't as invested in the relationship as she is... whatever the reason... the bottom line is this move on her part becomes the lesser of the two evils for her to take.
I think you've made a mistake.
So she was a little b1tchy on Saturday... hey, she turned it around sat. night, didn't she? And she's apologized for it, and she's offered to make you dinner. If her b1tchiness was all the time, I'd say yeah, get out. But if that was just a passing mood... otherwise it sounds like she's a great person. We all have our moments.
So WHAT if she acts lovey around you? It's not like she just met you last week and she's a nutjob, she's GROWN to have feelings for you because she's been dating you for several months. And when you made things official, she was HAPPY. Let me ask you, whose idea was to be boyfriend/girlfriend? Hers, right? She wants you.
Just tell her you didn't want her to catch whatever nasty bug you had. Tell her you'd really love a home cooked dinner. Try to keep this one around.