There is no 'one way' of coping. Everyone copes in different ways. And you mourning this little boy shows what kind of caring and compassionate person you are. I mourn for all my friend's children. I mourn for children I don't know who passed away.
You can use your grief for Adam for good things also. Teach your son water safety. Three years old is plenty old enough to start learning the rules of using a pool and being around water.
I'm so sorry to hear about you and your friends loss