My about to be 3 months old baby keeps sucking his fingers, even if he his hungry or not, what to do? Whenever I stop him from sucking he keeps crying. I tried using mittens but he keeps sucking even mittens. 3 days ago even though I cut his nails he injured the hard palate inside mouth with his fingernails and there was blood, therefore I am afraid of letting him suck his fingers anymore. Any suggestions would be greatly appreciated.