Ear wax is actually a good substance in your child's ear to help trap dust particles and dirt to keep his ears clean. Over time it dries up and moves to the external ear canal and drops out on its own. Build up occurs when the ears are unable to expel more than the ear wax is produced. I believe that is your issue.
You should not dig them as doing so will cause the wax to be pushed further in. Same thing goes for adults. You can either go to a doctor to flush it out if it causes discomfort or do so at home with ear drops (check that it is suitable for use with your toddler's age).
On a daily basis, just clean the external will do.
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