Neuroticism? I think you are confusing this with other issues. This need not even be mental health related. It simply could be a learned response based on prior events.

Let us assume for a moment however that this could be a mental health problem. My thoughts immediately think Anxiety and/or Depression. The root of these may lie in poor self-esteem and a lack of self-worth.

I believe you need to consider what exactly is triggering these thoughts to begin with.

If it is a self-worth issue, she will need to work this out obviously and with a little help from yourself. This doesn't mean constantly telling her she is beautiful, etc (there comes a point that being told this over and over again makes it no longer believable). It means drawing attention to and celebrating the little 'wins' in her life. Having a successful day at work might translate to saying, "I am proud of you." Making a meal could turn into a simple, "I really liked this." Even the offer to share doing things is a sign of appreciation, for this - sending her the signal she is APPRECIATED is the single biggest and most important act you can do.

Finally, I must ask here about your own habits. You may need to evaluate what your own actions may be signalling to her. For instance, communicating often with women that aren't her is a big red flag in my own books - particularly if any of these women are confidants. She has got to be your priority. Texting other women, etc might need to be curbed if this is a deal breaker for her - which she has every right to insist upon. This could in fact break the deal. What I am really trying to say here is that her boundaries need to be observed. If you cannot respect them then you need to consider if the relationship is right for you. This goes the other way too so that the two of you need to make your own concessions and come to an agreement.