No, you should not feel pain. If you do, speak up so your doctors can help you!
Your obstetrician and anesthesiologist will make sure you are comfortable before your C-section begins. If you feel any pain, they can adjust your epidural, administer a different kind of local pain medicine (such as a spinal), put you to sleep, or give you medication in your IV if need be.
It is entirely normal to feel the sensations of touch, movement, and pressure (which can be intense at certain points, such as when your baby is being delivered), but you should not feel pain. If you do, you need to let your doctors know so they can make you more comfortable!