Becoming monarch didn't depend on your age but rather on whether you were in line to the throne. Yes, in real life, there were child monarchs.
They didn't rule until they became adults. In the meantime, regents were appointed, to handle the duties of the monarchy until the child monarchs grew up. However, they certainly had the status of monarchs.
One example was Richard II, grandson of King Edward III of England. His father died before becoming king, so when his grandfather died, Richard himself became king at the age of 10.
You may be sure that people DID bow to a child monarch, even if the child wasn't yet allowed to reign on his own. Movies and fantasy books are not real life.
Louis XIV of France became King at the age of 5. Over 70 years later, he was succeeded by his 5-year-old great-grandson.
There were certainly medieval royal dynasties. Look up the Plantagenets for starters. Your problem is that you are not reading serious history books. Again, fantasy isn't real history.