Is it normal to have very bad nerve pain in lower jaw day after upper molar cavity is filled?

No.: Upper and lower jaws are supplied by separate branches of trigeminal nerve. What is done to one branch is usually not reflected in another branch. More likely your temporal mandibular joint was strained. Of course people with bad maxillary teeth are more likely to have bad mandibular teeth.

Check the bite: My best guess is that the filling done on the upper tooth may be a little high which is interfering with your occlusion or bite. The treated tooth and/or the opposing tooth have the potential to be sensitive if the filling is not adjusted correctly. Your dentist should be able to measure for a high spot and adjust accordingly. Try that first.