Is it normal to feel pain when touch after crown replacement ? (photo)

Pain from your new crown is not normal.  Perhaps there is still infection and the root canal should be evaluated.  The x-ray as posted does not show the end of the roots and root canal.  The other possibility is that the tooth is hitting too hard when you chew, and if that is all it is it will be an easy adjustment at the dental office.

No, it is NOT normal for a tooth to be painful to touch after crown replacement, especially when there is no nerve in tooth (root canal). Dentist should be checking your occlusion (the way your top and bottom teeth hit eachother when your teeth come together).