The medical exam is not incredibly detailed. Its basic purpose is to get a good basis of a character's health so that if the need arises they can be treated adequately later on, and to make sure that they don't carry any diseases with them that Starfleet isn't prepared to deal with an outbreak of. It's just a little IC precaution, though the exam can detect any physical history like broken bones or extraordinary biology (for example, when taking Trance Gemini's temperature it was revealed she was a sun avatar, which caused something of a stir). People can ask any questions they'd like during the exam, about the components of certain medication injections or what they're given for, too. He will get answers, though we can't guarantee it will all be written out by the individual medical mun you get.

As far as the pets: since they can also carry diseases or infections, they are subject to the same scans as their people.