I think the only reliable way to tell if any Sim has read a book is to have them read it again. A child or older Sim will give you the option to reread instead of read. I'm not sure about this for a toddler though. However, if a toddler Sim has already read a particular book, the metric bulb thingy will not appear. If a toddler has not completed a book a partially filled metric bulb will appear instead of an empty one. Skill tabs are not available for toddlers so the only way to know is whether the metric bulb thingy appears.
One quick way to check a toddler's book reading is to go to the library. Give the toddler the books one by one and you'll find out quite easily which books have already been read. Also, in the library, the Sim (even those without the bookworm trait) read books very quickly.
As for skill books, use the 'read' interaction, not the 'browse' on the library bookcase. A Sim cannot reread a skill book that they've already read or has passed that skill level. For instance, the first cook book becomes useless once a Sim has reached level 3 in cooking even if they've never read the book, having gained the skill by experience. Check the skill tab for how much skill the Sim has and direct them to the next book. Book I for levels 0-3, book II for levels 4-6 and book III to complete the skill.
I hope this is helpful.