My 3 month old Baby drinks every 3 hours at night, but when it comes time to put him in his crib he bcomes anxious and he scratches his face
It sounds like he is just starting early and protesting bedtime as most kids do.He might not like to sleep in his crib especially if he is used to falling asleep in your arms.
My guess is that the real concern is him scratching his face. You can get little mitts to put on his hands so he doesn't end up with marks on his face.
Clip his nails & get some mittens to cover his hands. He's just a little unhappy that he's not cuddled up next to you. It will pass if you consistently put him in bed after you feed him. He just has to get used to it.