Is it wrong to feel guilty about having someone else care for my baby?

No. I think it's natural for any parent to feel some guilt initially when leaving his/her child with another caregiver. I went through this myself with my kids. What is important is the time you take in finding the right care giver or care setting for your baby. This will help you feel the most secure in your decision. Take time if you can to drop in every now and then to observe how things are going.
No. Is it wrong? No. That means that you wish you were doing it. Most of us should feel that way. I feel a little guilty leaving the house every day. Should you be disabled by it? No, not necessarily. If you have to work, or have important tasks at hand, help is fine as long as you are giving them the attention and love they need, and making sure the other caregivers are also giving that love.