Blood may not "show", but it will wet their clothing and that will show, and any physical examination is likely to be either without the shirt, or the doctor or nurse will use a stethoscope under the shirt. Our doctor, examining my wife, always puts the stethoscope under her shirt, against the skin.
Their hand or instrument will come back bloody. They may notice the wetness on the black shirt. Try it. Pour a shotglass full of water on a black shirt, and see if you can tell the difference. I certainly would.
Even for a hit head, if somebody passed out the doctor is going to check their ribs for bruises, and their limbs for range of motion, to see if anything is sprained or bruised. Is your character not going to even wince? Because the doctor will be watching for that.
If your character is female, do not think this won't be done. She'll get either a female doctor, or a female nurse will be in the room as a witness.
As the author you clearly want these injuries to be discovered, so just make sure this routine examination for a fall is the way they are discovered.
Observed wetness of the shirt, observed pain when pressed or touched, and observed blood on the doctor's hand or instrument when using a stethoscope to listen to the lungs or heart.
These are all plausible routes to discovery that nobody that has been examined by doctor is going to question. The heart in particular could be the culprit, a reduced blood flow could cause the victim to pass out and hit their head.
And if they do an electrocardiogram, as is quite routine in a standard physical exam, the shirt comes off completely so the dozen or so sensors can be taped into place. I get one every year as part of my normal physical, and so does my wife for hers.