どこか痛みますかって英語でなんて言うの？

"Where do you feel pain" is asking the hurt/ ill person the location of where it hurts so that it can be taken care of appropriately.
"Are you hurt" is asking the ill/hurt person if they feel any kind of pain.
"are you in pain" is another way of asking the person if they are hurt or feel hurt anywhere.

"Does it hurt?" is the most direct way to ask if someone is experiencing pain. Usually you would use this if you already know which part is potentially injured or that they are feeling unwell.
"Do you have any pain?" is a general way of assessing if someone is experiencing pain anywhere in their body.
"Where does it hurt?" is something that would be said to narrow down which part or parts are causing the person to feel pain or to feel unwell. This can especially be said to children who are hurting or sick.

Obviously, the type and scale of someone's ailment must be taken into account when forming a question relating to pain. Is there an injury which is visible, or is there no apparent sign of injury?

If the person is unable to move they may be able to simply tell you where their pain is, and then you may be able to help.
The second answer implies that the person has the use of their limbs and can show you where they have any pain. It is important to identify where and the why pain is being caused, sometimes it is more obvious (broken leg) but sometimes if the problem is internal it can be tricky to diagnose.

When someone is not feeling well or ill then you would be worried and would want to try and help them so you could ask them 'are you in pain?
To find out where they are sore then you could ask 'where is it hurting?'

If someone seems to be ill or is hurting somewhere and you would like them to expand on this and explain further, you could say any of the following: "Does it hurt?", "Are you in pain at all?" or "Show me where you are hurting so I can help". All three of these examples would adequately help you find out more information about someone's illness or pain.