What doctors did your pediatrician recommend we see at our age?

What doctors did your pediatrician recommend we see at our age? I thought we'd be referred to a neurologist, surgeon, orthopedist, for example, like at 3 months old, to get checked or something general, but they sent us to an ophthalmologist and a dermatologist only. What doctors should we see in case of anything, or do an ultrasound? I'm just afraid that suddenly the child is sick, or God forbid something is wrong with their body, I want to make sure everything is okay...