Is picking your child up by both hands extremely harmful?

Certainly can be: Most infants, toddlers, & pre-school kids can easily dislocate their elbow if lifted that way or by a forearm. The pain they experience will raise the roof. An evening in an urgent care center or emergency room is a likely outcome. These kids should be picked up by their trunk. By the time that is not a likely injury they are so old you wouldn't want to lift them anyway.

No: Generally speaking, the answer is "no." there is a condition called nursemaid's elbow that can occur if a child is quickly lifted by the hands. This results in a subluxation of the radial head. This is easily treated by a pediatrician, er physician or orthopaedist.