How can I tell when my kid is really hurt?

Emotionally sensitive kids can overly react to physical and emotional trauma. It is not that they are malingering, they actually are supersensitive to pain. Small bruises and cuts can make them feel as if they have broken their bone.
It sure can be very difficult to evaluate if the injury is really severe or it has been overly felt by the kid. A slight misjudgment can put the child in a potentially dangerous situation.
First key to manage such situation is to be empathetic. Don’t be judgmental, make the child feel comfortable and give him the assurance that you know he is really in pain. If he senses any frustration or mistrust in your words, his behavioral response can further aggravate.
I have met parents who attended first aid courses so they could be well acquainted with required first aid procedures. It also helped them in making an informed decision about taking the child for emergency support in hospital or not.
I think if parents feel confused, they should not take any risk with child’s health. Taking help from an online medical support facility (e.g. via video call etc.) can be a good way to arrive at a better decision.

What you describe seems to be a child with high sensitivities. His emotions are just as big and finely tuned as his physical feelings. It may be a benefit for you to look into him taking a specially-designed for kids identifier test to see if he falls into this category.

Dr. Elaine Aron has conducted years of research on highly sensitive persons, or HSPs, and has helped countless parents become better equipped to help their children understand and manage their high sensitivities. I highly recommend looking up her findings.

Being an HSP means that your body can genuinely feel a more intense pain from the seemingly most smallest injury. Literally, a papercut which most people can brush off after about 30 minutes, can affect an HSP for hours. Your son may honestly be having a more intense reaction to an "injury" because that is what he's really feeling.

He may also just be more inclined to being over dramatic, so that's also a possibility :-) So I would say to look into the possibility of him identifying as an HSP, and then he could have some tools to manage it.

You describe my 8-year-old grandson to a "T". He too is very exuberant about much of life and is such a fun boy! However, when hurt, it sounds like it is a near-death experience! I would think that he would be embarrassed by his behavior, but he is so wrapped up in the moment that he does not care. We hoped he would outgrow this dramatic behavior, but your story makes me wonder.

As a pediatric nurse, I can pretty much ascertain if he is truly hurt or not. Working as a school nurse has taught me not to panic when there is screaming and tears.

I recommend that you calmly assess him after an injury. If not severe, play down the injury but also offer a few soothing words like, "you are fine and will be OK". Have him relax a bit, and then once he calms down, he will usually be able to use the injured limb fine or get over whatever was wrong.

I was usually busy in my school clinic, so I just offered them a book or LEGOS once I felt they were OK, and soon they forgot about their injuries with all of the distractions in the room.