Hello. I have been a Medical Assistant for many years in Internal Medicine and Pediatrics. It is absolutely normal for some people to have more earwax than others, even if there is not a family history of it. There is a medical term for excessive earwax buildup: otorrhea. If you are concerned about this you should consult your child's physician. You should also seek that doctor's advice about cleaning your child's ear. It is not generally recommended to clean a child's ears with a Q-tip. One of the reasons for this is that you can actually push the wax down into the ear canal toward the eardrum, causing an impaction against the eardrum and in extreme cases, hearing loss. A good way to gently clean wax from your child's ear during bath time is to gently wash the outer portion of the ear while you wash the child's hair, and then tilt the child's head to drain any water (and loosen and wash out the wax) out of the ear. That is sufficient to clean out normal wax buildup. (If the wax is sticky it may take a few baths to get it loosened and "moving", so you may have to keep working at it, but be patient and don't give up.) For children with large amounts of wax buildup, there are ear drops that can be prescribed to help break up the wax, as well as other methods that your child's doctor can discuss with you to help with the situation. In many cases the child may grow out of the issue and it will not be an embarrassing problem for him/her in later years. The rule of thumb for when to talk to a doctor about ANY medical issue is that if there is anything that goes on for more that 2 weeks, talk to a doctor; if there is something that is below the surface of the skin that you are not sure about, talk to your doctor. That is what they are there for. If they make you feel like you are bothering them to ask, find another doctor.
I hope that I have helped you. Please do not hesitate to ask if you have any other questions. Best wishes!