Considering the baby being 3 month old … there are 2 possibilities.
If the movements stop in sleep or touching the hand… and if it disappears in 3 more months… we may call it normal…
Though it is difficult to imagine without a video… the way you describe these movements may suggest choreoid movements and may need an mri
scan of brain.
Occasionally some seizures do mimick this hence an eeg test may be important to rule this out.