Eye Problem Palsy

My son holds his left hand a tight fist often. Does he have cerebral palsy?
My son is two and a half months old. He often bends his left arm unto his chest or tummy with a pretty tight fist at the same time. Meanwhile his right hand could be doing the same thing. But most of the time, the right hand is more relaxed and open. We did not realize this until we went to see our doctor last week for his first needle. His Dr. said that it might be a sign of cerebral palsy. So we have to keep an eye on him. It is very upsetting, but it may be too early to be diagnosed. I wonder if anyone’s baby has the same problem but turned out to be perfectly normal. Thanks.
My son actually held his arms straight out (up?) away from his chest with hands clenched quite a lot at that age. There was nothing the matter with him. He looked like he was doing reverse push-ups.
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