Hello, I have read your question and understand your concerns. At 3 months of age, infants are described as “hatching” socially, becoming interested in a wider world. During feeding, infants no longer focus exclusively on the mother, but become distracted. In the mother's arms, the infant may literally turn around, preferring to face outward. Although each baby develops in her own individual way and at her own rate, failure to reach certain milestones may signal medical or developmental problems requiring special attention. If you notice any of the following warning signs in your infant at this age, discuss them with your
pediatrician.
Doesn’t seem to respond to loud sounds
Doesn’t notice her hands by two months
Doesn’t smile at the sound of your voice by two months
Doesn’t follow moving objects with her eyes by two to three months
Doesn’t grasp and hold objects by three months
Doesn’t smile at people by three months
Cannot support her head well at three months
Doesn’t reach for and grasp toys by three to four months
Doesn’t babble by three to four months
Doesn’t bring objects to her mouth by four months
Has trouble moving one or both eyes in all directions
Crosses her eyes most of the time (Occasional crossing of the eyes is normal in these first months.)
Doesn’t pay attention to new faces, or seems very frightened by new faces or surroundings
My opinion would be to consult your Pediatrician who would further advise after examining the child.