A perforated tympanic membrane (aka TM or eardrum) by definition has some sort of tear or hole. I could see someone making a presumptive diagnosis based on visualization of blood or blood-tinged fluid in the outer ear or a careful medical history though.
Re how long to wait, middle ear (and by extension, Eustachian tube) inflammation caused by barotrauma is notoriously slow to resolve. It can take even longer than Dr. Google says. If you decide to dive again, you will need to be very mindful of your equalization technique, which from your description probably needs some fine-tuning. There's excellent advice above on how to properly equalize, and to reiterate part of it, you must never force a Valsalva (pinch the nose and blow) maneuver. Doing so can result in serious, possibly permanent injury to your inner ear, which contains the delicate structures involved in balance and hearing.
Best regards,
DDM