If you have any questions or doubts about the person who is helping you care for your baby, trust your instincts and terminate her employment. Trusting your nanny is essential to the well-being of your child and to your peace of mind. You need to feel comfortable about allowing this person to be alone with your child. If you do not, then find a suitable replacement as soon as possible. You might consider asking friends and co-workers to recommend a nanny.
Personal referrals are usually the most reliable ones.
If this is not possible, then be scrupulous about checking references, run a complete background check including fingerprints, and find someone that you feel you can trust with your precious little one. Best of luck to you, and no, I do not feel you are being paranoid. You are being a good mother.