I understand what you mean. When my daughter was an infant, I used to have waves of panic come over me thinking about what might happen if something happened to me. Amidst my sobs I would give very serious instructions to my husband on what to do if I died or was seriously hurt. (First on the list was to call LLL and get my baby some breastmilk pronto!

) I just felt SOOO responsible, and it was very overwhelming and scary.
Now DD is almost 3, and there are still times when I feel anxious about the responsibility, but it's somewhat different now. She is older and has developed some independence, plus has formed more attachments with other people, so it doesn't feel as much like she is dependent solely on me. I can only imagine that this shift will continue over time as she becomes more and more self-sufficient.
If you are worried about any feelings you are having, then I would highly recommend seeing a therapist. My therapist (an AP mom herself) has helped me to work through the amazing but overwhelming and anxiety-causing changes motherhood has brought. It's so much change to assimilate in so little time.
You are not alone in feeling scared and overwhelmed, but the fact that you are so aware of and concerned about your feelings tells me that you are a loving and conscientious mom. Don't be afraid to talk about the challenges you face. Most people won't broach the subject themselves because our society has this myth about how parenting should be -- but in my experience LOTS of moms I know have had very similar feelings to mine. It's reassuring to find that you're not alone!
Warmly,
Carol